The Gunners hope to recover from a disappointing opening Group F defeat away to Dinamo Zagreb, where striker Olivier Giroud was sent off.
Given their next European fixtures a double-header against German Champions Bayern Munich, the Arsenal manager knows there is now little 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.
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“We cannot afford to drop points now against anyone at home.”
Greek league leaders Olympiakos and Arsenal are in the same group for the fourth time in seven seasons, although they have a terrible record playing away to English clubs in Europe.
Wenger, though, is not expecting an easy ride against the Greeks.
He added “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, with Wenger insisting it is as a result of the intensity of the Premier League.
He said “It is true that mentally you cannot ease off before a Champions League game as some others can.
“Olympiacos won comfortably on Saturday, when we were in a high intensity game at Leicester, they were safe after 20 minutes.
“Dinamo Zagreb played on Saturday and they took three players off at half-time. I cannot do that at Leicester.
“For sure the Premier League is demanding and consuming energy wise, mentally more than physically because physically you recover.”
The UEFA Champions League resumes on Tuesday with Defending Champions, Barcelona play host to German side, Bayer Leverkusen and former champions Bayern Munich at home to Dinamo Zagreb of Croatia.