By ESPNSTAR.com staff
Zenit launched a superb fight back to recover from two goals down but the Rossoneri still managed to eke out a win 15 minutes from time via an unlucky Tomas Hubocan own goal.
It was a morale boosting victory for Allegri's men against a spirited Zenit side and it gives the Rossoneri some momentum coming into their upcoming Milan derby against Inter Milan on Sunday.
The importance of the victory is not lost on Allegri, who praised his side for being able to pick up the win despite facing some difficult moments.
"The players looked for the win and they got it by suffering for it after a good first half," Allegri was quoted as saying by the official AC Milan website.
"We continued to play football even after the Russians came back into it."
Allegri also hailed goalkeeper Christian Abbiati, who made a string of fine saves to deny Zenit, and highlighted the importance of having different tactical options to choose from.
"The players did well especially Abbiati in a couple of circumstances," Allegri added.
"We played well for 20 minutes and with Bojan we play in a different way.
"He's more of a technical player than Pazzini who was in any case decisive for the third goal.
"I maybe should have played 3 in the middle after half an hour when we had problems getting out of our half.
"I think that having different tactical options is important. We have to learn to read different parts of the game and that happened tonight [Wednesday].
"Now we have three days for the derby and we'll hope to have all the right ingredients for such an important match".
Milan may have made a stuttering start to their season but playmaker Riccardo Montolivo believes this win over Zenit proves the team's immense ability and is already looking forward to the Milan derby.
"We needed to get a good result away from home and we got it.
"We started off really well and the we conceded a bit of space but we did well not to give in.
"I think this is a team that can change things around with the game in motion and we have a few different options.
"I already have goose bumps on my skin thinking of my first derby".
Milan currently lie second in their Champion League Group C on four points while Zenit remain rooted to the bottom having failed to pick up a single point in their two games so far.