Second-half goals for Jack Wilshere – his first in almost two years – and Lukas Podolski made sure of at least second place in Group B after leaders Schalke '04 defeated Olympiakos 1-0.
Wilshere was under no illusions that Arsenal need to improve if they are to make an impression on the Champions League after they progressed to the last 16.
Wilshere knows that they have to get better and said: "We started off sloppy but we've still got one game left. We need to finish top.
"The first half was hard – we were sloppy, we gave the ball away and weren't ourselves so we needed to come out in the second period and get an early goal."
He added: "We have to step it up. Tonight wasn't good enough, especially in the first half. We've got to play the best teams to win it so it doesn't matter who we get."
Podolski echoed Wilshere's sentiments, saying: "In the first half, we lost a lot of balls.The first goal from Jack came at a good time for us. We were after three points and we are happy to have done so."
Arsene Wenger's side must now beat Olympiakos in Athens in a fortnight to stand any chance of finishing top and so head into the last 16 as one of the seeded sides.