"We won a difficult and important game, as we needed this win after three matches with just two points," Football Italia quotes Allegri as saying. "We also kept our first clean sheet.
"There was no need to shout [at half time]. At the moment when things are going badly you just need to reassure the lads. They have been putting in the effort and it's a question of centimetres between a goal and a wasted chance.
"I think the players should be complimented, as even in difficulty and tired they were able to control the game."
Milan are now eighth in Serie A ahead of tomorrow's fixtures.