Claudio Marchisio scored two late goals to hand Juventus victory over AC Milan in Turin, while Milan had Kevin-Prince Boateng sent off for a second bookable offence and Marchisio notched his second in injury time.
The result lifted unbeaten Juve to the top of the standings, level on 11 points with Udinese.
Milan, on the other hand, have just five points from five games.
Allegri, speaking to his club's official website, admitted his side had made "a lot of mistakes".
The Italian said: "Juve caused us a lot of problems and we made a lot of mistakes.
"We didn't react well and we conceded when the game looked like it was finished. But the truth is they knew how to put us in difficulty. There was that half rebound at the end and we paid for it. We were definitely a bit unlucky as well.
"The main dangers came from the runs from the midfield which caused us problems, But Milan will be back, and we'll start again without panicking", he added.
"I don't think there is a psychological problem.
"We weren't as sharp as we could have been against Juve.
"We didn't play well in defence or in attack.
"But there is nothing to worry about."
Striker Zlatan Ibrahimovic, who missed the last three league games through injury but returned to the line-up to face his former club, added: "It was a tough game, they were better than us. The result is the right one. The were better on all levels.
"We didn't get our game together. Congratulations to them for a game well played, We'll get back to work after the international break. We've had a lot of injuries including Pato, Robinho and many others. We're as good as we were last season, that's for sure, we just need to be patient.
"When we get our rhythm back, we'll beat them all", the Swede concluded.