Peter Crouch scored the only goal of the game after a rapid break by winger Aaron Lennon and Milan struggled for fluency, though they did test Heurelho Gomes with two headers from defender Mario Yepes.
The match descended into chaos at times during the second half as Gennaro Gattuso grabbed Totenham's assistant manager Joe Jordan by the throat and then aimed a headbutt at him after the final whistle.
But Allegri dismissed the incident telling Sky Sport Italia: "I didn't understand what happened there. It was just a scuffle, nothing serious."
However, Gattuso later told La Gazzetta dello Sport: "I lost my head. I was wrong. There is no justification for what I did. I'm not going to say what was said, that's between us, we were speaking Scottish. Do I expect a ban? I'll accept whatever I get."
Meanwhile, Allegri maintained Milan's defeat was "undeserved and qualification is still wide open."
He added: "We are paying the price for the mistake we made on the counter-attack.
"We were looking for the goal against Tottenham, who defended very well and it was difficult to find space. In the second half we played further up the pitch and created chances. We were too timid before the break and didn't attack Tottenham properly.
"We'll need a different approach in London, which we did see in parts in the second half tonight. It's difficult for anyone to play when Spurs come to San Siro and close down all the spaces. You've got to give credit to Tottenham for their defending."
"Up until now Ibra has always done great things. This isn't the match to judge whether he's had a good or bad season in Europe."
Allegri confirmed goalkeeper Christian Abbiati was having tests at hospital after he was substituted in the first half for concussion.