Arsenal, who have recently endured problematic defeats to both Manchester City and Brighton & Hove Albion, were able to earn two crucial away goals in Milan, as Henrikh Mkhitaryan and Aaron Ramsey secured a comfortable win at San Siro.
"It is an important win of course after we had a nightmare week," Wenger told BT Sport. "Overall it is important to win, but it is not qualification. We have to finish the job at home. I am happy with the spirit and response we gave.
"We were not in a position to take risks, but we could not be too cautious as you lose fluidity. We defended with resilience until the end.
"When you play in a cup final it is hard to digest in a few days. When you are knocked down like a boxer you don't have time to react and you are only halfway up, but you have to respond. Your pride and desire to show quality has to come through in the game."
Arsenal will now take their two-goal advantage into next week's return leg at the Emirates.