The Gunners host the Greek leaders, who have won all of their five domestic fixtures, needing to recover from a disappointing opening Group F defeat away to Dinamo Zagreb, where strike Olivier Giroud was sent off.
With a double-header next against Bayern Munich, Wenger concedes Wednesday's contest now leaves no margin for further error.
He said: "You have to win your home games if you want to qualify from the group stage, it is simple as that.
"We cannot afford to drop points now against anyone at home."
Wenger added: "Olympiacos dominates their league, they are a team with a big advantage - they dominate their league easily, so they can prepare for these kinds of games.
"They are well organised and have some players who know the Premier League, like (Esteban) Cambiasso and (Pajtim) Kasami who both played in England."
It has been a poor start for English sides in Europe's elite club competition this season, with defeats for both Manchester clubs as well as Arsenal.
Wenger, though, does not believe any definitives can yet be drawn.
He said: "The Premier League is very, very tough
Is that an influence or not? I don't know, but it's a bit early to come to any conclusions
We have to wait a little bit longer.
"A second year without us being successful and you could come to a conclusion of, 'yes, there is something we have to analyse deeply', but I don't believe so at the moment.
"Are we far away? I don't think so, but we have to show that with our performance."
Arsenal host Premier League leaders Manchester United on Sunday, but that will not impact on Wenger's team selection, although goalkeeper David Ospina could again be preferred to Petr Cech.
Wenger said: "We play on Tuesday night and then Manchester United on Sunday, five days is no problem
It is more about what happens before.
"Some players had two tough games at Tottenham and at Leicester where they were a high level physically
I will have to analyse that and make my decisions."
Defensive midfielder Francis Coquelin has returned to training following a knee problem which kept him out of Saturday's 5-2 win at Leicester.
Forward Alexis Sanchez netted a hat-trick to help sink the previously unbeaten Foxes.
Midfielder Alex Oxlade-Chamberlain believes everyone can learn from the tenacious approach of the Chile forward.
He said: "Alexis is one of the most passionate and hungry individuals I know
As a player, he brings out the best of you in training every day and also in the matches.
"It is his everyday mannerisms around the training ground, how he trains, his performances, how he scores goals, how he plays and how he defends from up front, these are all things that we can all learn."
Wenger wants England international Oxlade-Chamberlain to have more self belief.
It is an area of his game the 22-year-old has heard needs improvement before
He added: "It is what my dad says as well so there might be a little bit of a trend here.
"I am quite critical of myself and I try to demand quite high standards of myself, so sometimes maybe that can work in a negative fashion and is something that I need to work on."
Source : PA