A Robin van Persie double gave the hosts a 2-0 lead, before Japanese attacker Shinji Kagawa pulled back a late consolation for Jurgen Klopp’s men.
The Bundesliga holders suffered injuries to key midfielders Mario Gotze and Sven Bender in the first half, and now look doomed to be eliminated from the competition.
Arsene Wenger was pleased with his team’s performance, and especially at topping the pool given the fact that his side were in a difficult group.
“Overall I am very happy. We were in a very difficult group and you can see that tonight with Olympiakos winning in Marseille,” the Frenchman told Sky Sports.
“Therefore I am very proud that we finished top of the group.”
Wenger has full of praise for his Dutch goalscorer also, and believes that if he continues his rich vein of form he could be comparable to Lionel Messi or Cristiano Ronaldo.
“If he keeps going like that of course.
“Let him play and see at the end of the season. He is the leader of the team as well so what is important is that he leads the team to success.
“I feel he is an exceptional player and I’m happy he can show that,” he concluded.
Arsenal now host Fulham at the Emirates Stadium on Saturday, and will look to move closer to the top four places with a win.
By Gareth McKnight