Well, drop points they now have, and what previously was thought of as a given -- Arsenal's qualification for the round of 16, the phase of the competition in which they have been fixtures for as long as many of their fans can remember -- is very much in jeopardy.
Last season, Basel managed to make it through to the knockout rounds with seven points, while others progressed with eight. Even if that lower threshold is taken as the total that Arsenal must reach to qualify from this group, then they need to win two of their remaining four games, and get something from the other two.
When put like that, it doesn't sound like an especially strenuous ask, but then you remember that two of those games -- the next two, in fact -- are against Bayern Munich. While Arsenal were huffing and puffing against Olympiakos, Bayern were hammering home goal after goal against Dynamo Zagreb, against whom the Gunners lost two weeks ago.
There was some debate about two of the Greek visitors' goals in this defeat. Their second, credited as an own goal against David Ospina, initially looked like it had not crossed the line, but later replays showed it definitely had. It was awarded by one of the goal line officials, who had a pretty good view and got his decision spot-on. For the eventual winner, scorer Alfred Finnbogason looked offside as the ball was played through to Felipe Pardo, who then crossed for the substitute to clip home.
However, the Greek side deserved the win. They defended stoutly, particularly when an absurdly impressive double-stop early in the second half from goalkeeper Roberto was followed by a block on the line by Omar Elabdellaoui.
Olympiakos always looked threatening on the counterattack, too. Pardo, Seba and Leandro Salino were particularly impressive, with their collective pace troubling Arsenal throughout. Most crucially of all, they were clinical when they had chances, while Arsenal were not.
Against all the odds, Olympiakos now have a better chance of making it through to the knockout rounds than do Arsenal.
Arsenal equalised twice but could not find a way back into the game for a third time.2. Familiar failings
It's sometimes easy to wonder why Arsenal -- perennial Champions League participants, permanent residents in the top four of the Premier League and a team who have won major trophies in the last two seasons -- are the subject of so much criticism, even ridicule.
But then, all you have to do is watch them put in a performance like they did on Tuesday. This was almost a parody of Arsenal. They dominated possession, but overplayed with the ball too many times around the edge of the Olympiakos box before their alarming defensive brittleness saw them concede from the relatively few attacks their visitors had.
Arsenal were not objectionably bad, but they still managed to come away with nothing. It's said of some teams that they just find a way of winning, but Wenger's side will often manage to find some way of losing. What has been done will be done again; there is nothing new under the sun. At least where Arsenal are concerned.
It's part of the reason that there will always be a school of thought that Arsenal will not win either the Premier League or Champions League while Wenger is in charge, because these problems are habitual. It almost doesn't matter which players are actually on the pitch; the team will always do the same thing.
There wasn't a great deal Arsenal could have done about the opening goal, scored via a hefty deflection off Alex Oxlade-Chamberlain, but the second was very preventable indeed and the third came immediately after Alexis Sanchez had made it 2-2. When Arsenal are good, they can be electrifying, but when they are bad, they are utterly infuriating and masters at being unable to prevent the very preventable.
David Ospina's own goal drew into focus the decision of Arsene Wenger to start the Colombian over Petr Cech.3. Ospina drops the ball
It's always a bit of a debate as to whether resting your first-choice goalkeeper and giving the backup a few games is a wise move or not.
On the one hand, it's theoretically shrewd to allow the No. 2 time between the sticks so he stays sharp for when he is genuinely required. It is a chance to ensure, in these days when reserve teams aren't really a thing, that he doesn't just spend his entire life sitting on the bench.
On the other, a backup is a backup for a reason and it shows when he does things like, say, dropping a routine corner over the line when under minimal pressure from opposition strikers. Ospina, drafted in to give Petr Cech a breather, did exactly that against Olympiakos, following a not entirely convincing performance against Dynamo Zagreb in the previous game.
There was some talk that Cech had a calf problem, but none of that was mentioned by Wenger before the game and it does seem to be an unofficial policy that Ospina will play in cup games, while the Czech takes league duty.
All of which is fine, but it does seem rather odd to make a significant purchase like Cech, presumably in order to improve Arsenal overall and make them more competitive in competitions like, one would imagine, the Champions League, then leave him out for the first two encounters in Europe.
Much of the hope surrounding Arsenal in the summer was based around the recruitment of Cech, which looked like the sort of ruthless, short-term move we're not used to seeing from Wenger these days. That sort of hope, though, seems pointless when the new signing is not actually used.
There's no guarantee that Cech himself would not have made a similar error -- witness his howlers against West Ham in the first game of the Premier League season -- but the whole idea of spending £11 million on a 33-year-old goalkeeper is that those sort of mistakes are less likely.
It's rather curious, to say the least, for Wenger to declare this as a must-win game after their defeat in the first fixture and then not play his best available team.
Arsenal face Champions League humiliation after Olympiakos defeat
Arsenal manager Arsene Wenger stood by his decision to play David Ospina and rest Petr Cech after the Colombian goalkeeper's error contributed to his team's shocking 3-2 home Champions League defeat to Olympiakos on Tuesday.
The Premier League side were behind against the run of play on 32 minutes when a low shot from Felipe Pardo deflected off Alex Oxlade-Chamberlain, though Theo Walcott netted a quick equaliser.
Replacement goalkeeper Ospina then made a catastrophic mistake for the Greeks' second goal, inexplicably patting Kostas Fortounis's corner down behind his own line.
Arsenal recovered with an equaliser through Alexis Sanchez, though substitute Alfred Finnbogason quickly responded to give the Greeks a first win in England at the 13th attempt.
"Ospina played 19 games last year, kept 14 clean sheets," Wenger said in his postgame news conference. "Last week at Tottenham he had a fantastic game. No keeper is mistake-free. It could have happened to Petr Cech as well."
Wenger explained why he left sole summer signing Cech out, saying: "He had a slight alert before the game at Leicester [on Saturday]. It's not because of that that we lost the game. I make those decisions and the selections for the team and I am responsible for it.
"You cannot select the team by making a poll before the game and taking everybody's opinion."
David Ospina's error contributed to Arsenal's shock defeat on Tuesday.Wenger, who maintains that Arsenal can still reach the next round, said the blame for the defeat should be shared rather than single out his Colombian goalkeeper.
"There was a bit of bad luck as well," he said. "They had four shots on target and scored three goals.
"That happens once every 100 games in the Champions League. But we feel guilty because we gave easy goals away."
Aaron Ramsey and Nacho Monreal were also omitted in favour of Alex Oxlade-Chamberlain and Kieran Gibbs, but Wenger again defended his selection.
"You cannot play every three days without rotating your players," he said. "We played with [Santi] Cazorla, [Francis] Coquelin and [Mesut] Ozil in midfield. They play together six months. That's the team that plays always."
Wenger confirmed that centre-back Laurent Koscielny had to be replaced due to injury in the second half, adding: "A hamstring [problem]. We play many games and that's why we rotate."