A goal from Diego Milito in the 54th minute was enough to earn Inter all three points and take them to within six points of the Serie A summit and just five of their city rivals.
And Allegri admits Inter are now serious title contenders but refused to be ruffled by the defeat.
"Things remain almost unchanged - except that Inter have re-entered the Scudetto race," he told Sky Sport Italia.
"They did well, waited and stayed deep and we were not able to create much. We needed to unlock them by drawing them out to play because they had 10 men behind the ball but we could not do it."
Probed about Pato's stay at Milan, which brought an end to the pursuit of Carlos Tevez, Allegri revealed he had no say in the club's decision and that he never wanted the Brazilian to leave.
"I didn't make the decision on Pato. It was a club decision to keep the boy."
"But I never said that I wanted to sell Pato because Tevez would have replaced Cassano [out until the end of the season after undergoing heart surgery] and not Pato.
"I cannot tell you if Tevez could still arrive. Now we must stick together and pick up the pieces of a centre-midfield which now has fewer players seeing that [Kevin-Prince] Boateng is now suspended for the next game [against Novara]."
Milan are tied with Juventus at the top with 37 points but with a better goal difference.
They host Novara next in midweek.