The visitors were bailed out by an injury-time penalty from Mario Balotelli - a play that infuriated Torino boss Giampiero Ventura as he was refused a substitution at a stoppage moments earlier - but Allegri was not convinced by his side's form at the back.
"Four minutes from the end we'd lost this, but the lads did well to believe. Torino played well, caused us a lot of problems and we left ourselves too open to their counter-attacks," Allegri said.
Allegri praised Torino's forwards, with Alessio Cerci scoring once and providing an assist, while Ciro Immobile teed up Cerci for his goal.
"Alessio Cerci and Ciro Immobile had a good game in attack, while it was clear they could run at us and use their technique against our defence," the Milan boss said.
He added: "We have changed some things in our system, so it takes time to rediscover our balance. At the moment we are too soft in defence – by which I mean the whole team is not effective enough when defending. It's not good enough."
Fresh from re-joining the San Siro club from a stint at Real Madrid, Kaka appeared for 70 minutes - eventually replaced by Valter Birsa - but Allegri was content with the Brazilian's output.
"Kaka had not played for a while, though he showed great intensity and didn't hold back," Allegri said.
Allegri denied his side played outside the spirit of the game after they earned a penalty at the death despite Torino wanting to make a substitution prior.
"The ball was out of play, we had it and took it quickly," Allegri said.
"These things can happen. It's only natural that Toro feel robbed, as they were 2-0 up with a few minutes to go, but we played fair."
As they prepare for a mid-week UEFA Champions League clash with Celtic in Milan on Wednesday, Allegri said improvement was necessary as they go into the European clash minus Ignazio Abate, Riccardo Montolivo, Stephan El Shaarawy and Mattia De Sciglio.
