The Sweden international, 30, scored the fourth and final goal of the game from the penalty spot and assisted two of the others.
Szczesny, who was unable to stop the former Barcelona and Inter forward's spot-kick despite getting a hand to the ball, accepted Milan was the better team on the night.
“I think everyone was up for it, and they knew how to play the game, but they were the better team on the night and that's the story of the day,” the Gunners goalkeeper told ITV Sport.
“I don't think it's a surprise. They have some of the best attacking players in the world.
“When you're playing against Ibra, he's up there as the best striker we've played against. They had quality up front and used it very well."
The scoring opened early on when former Tottenham player Kevin-Prince Boateng smashed in off the underside of the crossbar, before a Robinho brace either side of halftime put Milan three goals up prior to Ibrahimovic’s effort.
However, Szczesny played down the woeful Arsenal performance: “We didn't have the best of games but you have to give credit to Milan.
“They punished us on every occasion; they scored some quality goals and they deserved to win.”