The Rossoneri coach was over the moon with his side's performance in Europe on Wednesday, but felt that they could have carved out an even bigger first-leg advantage
Goals from Kevin-Prince Boateng, Robinho and Zlatan Ibrahimovic helped the Rossoneri to a comfortable win at San Siro, yet Allegri has acknowledged that things could have been even better for Milan.
"My only regret is that we created a couple of good chances towards the end and didn't exploit them to extend our lead. I'm happy, of course, but if we had managed to score a fifth it would have been even better," Allegri said in his post-match press conference.
"We played well as a team, creating a lot and stopping them in a really good way. Our positioning was excellent and it prevented them from creating openings."
Allegri then warned his players not to become complacent as he continued to praise his team for stifling the north Londoners.
"Now we must keep working to improve and leave behind the difficult period we experienced before our last two games. Arsenal have a lot of quality both as a team and individually, and if they didn't show their class tonight [Wednesday night] all the credit goes to Milan."
The second leg is scheduled to take place on March 6. The Rossoneri return to Serie A action on Sunday with a trip to Cesena.