The Rossoneri won 3-2 at the Stadio Olimpico to secure their fourth success in a row.

"The important thing was to win today and we did that," Allegri said. "We needed to get three points at Roma to go further up in the standings and even though we suffered, we got the job done.

"I'm very happy with my players' display because it wasn't easy to beat Roma, a team that will be among the contenders for the scudetto."

Allegri highlighted the performance of his goalkeeper Christian Abbiati, who made a string of saves to deny Roma a late equaliser.

"Abbiati was extraordinary," Allegri said. "He made some very good saves in the second half.

"He has improved a lot this season and he still has room for improvement.

"He is an important player for Milan."

Allegri also showered praise on striker Zlatan Ibrahimovic, who scored twice tonight.

"He had an excellent game," Allegri said. "I'm very happy with his performance."

Roma, meanwhile, slipped to their third defeat in four games and coach Luis Enrique believes today's game exposed many of his team's weaknesses.

"We never had a chance to win this game," he said. "There was too much difference between Milan and Roma.

"We lacked the incisive cutting edge in the opening half and we didn't have the right concentration throughout the game.

"We struggled to defend from dead ball situations and allowed (Alessandro) Nesta to score Milan's second as though he was in his own house.

"We are not yet a big team and we must improve. We are lacking many things.

"Milan has a lot of experience and we don't."