The coach reiterated the need for his team to improve, but has called for patience regarding expectations surrounding Kaka's return
The plucky hosts surged into a two-goal lead that the Rossoneri took up late to claw back through goals from Sulley Muntari and Mario Balotelli, whose penalty came in stoppage-time.
Allegri was concerned that his men bared all their frailties on the night, although he admitted he was not surprised considering the circumstances.
"Torino deserve a lot of credit and we don’t. We conceded a lot on the counter-attack and we played badly technically," the 46-year-old told reporters.
"We did well [to draw] and we were lucky. The performance didn’t shock me, the team needs to be changed. Unfortunately we’re missing four internationals.
"We avoided the loss which would have been bad. Now we have to get back on track from the point that we got tonight and find the right balance."
Kaka failed to inspire Milan to victory after being handed his first game since re-joining his former club from Real Madrid, although Allegri has urged the public to allow the San Siro icon more time to deliver.
"Kaka, Balotelli and Robinho have never played together before," the Italian cited. "Kaka needs to get match fitness and to get to know his team-mates better.
"From the point of view of the commitment of the payers, it was a good match. The players did well. They tried to come back into the match and kept believing until the end.
"We have a very big month ahead of us but we can do it."
Milan host Celtic in their Champions League opener on Wednesday, before facing fellow Scudetto candidates Napoli next in Serie A.