Arsene Wenger's charges claimed two vital away goals in the first leg of their last-16 encounter, as Henrikh Mkhitaryan and Aaron Ramsey notched first-half finishes in order to hand the Gunners a comfortable victory on the road.
"We knew this was going to be a very difficult match," Gattuso told reporters after the game at San Siro.
"Arsenal were coming off a tough moment, but have enormous quality at their disposal, while we made too many mistakes. We never played like a united team and Arsenal deserved the victory.
"We could've done more, but we didn't play as a team, so every time they attacked, it was a danger. Playing at this level is new to many of these lads, so we look forward without losing confidence. It was an off day and Arsenal deserved it. We'll learn from this."
Milan will be hoping to overturn the deficit when they visit London next week, but first they must face Genoa in Serie A at the weekend.