"I think Milan played a good game and created many chances, allowing Juve a couple of shots from distance in the first half after we gave the ball away cheaply. We had plenty of opportunities to equalise, but the result certainly does not reflect what happened on the field. That's football," said Allegri.
"There was a mistake on a cross-field pass for Fabio Quagliarella's goal, but until that moment Juventus had barely got out of their own half. We didn't take our opportunities and were a little too hasty in trying to get the goal, so we paid for that.
"I think this is the first loss of the season where we really did not deserve it."
Milan have shown a tendency to struggle against the big clubs, as they were defeated 2-0 at the Bernabeu in the Champions League.
"This is a completely different match from Real Madrid. We have to accept the defeat in a calm manner, aware that we didn't deserve this and at the end of the season we will be challenging for the Scudetto," argued Allegri.
"Tonight there were some individual errors, which can happen, but we paid a heavy price, as we dominated for the first 20 minutes and then gave the ball away cheaply. We could've done a lot better in attack too.
"I am disappointed, as we conceded some avoidable goals and should've been more patient in spreading the play.