Juventus are yet to record a win in the Serie A this season after four matches, two draws and two losses.
With hopes of getting a first win against AC Milan, the Bianconeri failed to do so as they shared spoils on Sunday.
Alvaro Morata opened the scoring for Juventus with a 4th minute strike, before the Rossoneri found their equaliser in the second-half of the game in the 76th minute through Antic Rebic's goal.
However, Allegri believes he should take ‘responsibility for getting the substitutions wrong’.
“Despite a good first half, when we created chances and allowed Milan just one opportunity, we even risked defeat at the end of a game that had been under total control,” Allegri told DAZN.
“Unfortunately, we lost that concentration, determination and focus. Just look at the corner where we conceded the goal, there was complacency. It’s not possible to give this game away after being in control. Evidently, we need to make more progress. A lot more.
“This game doesn’t change anything in my view of Juventus. What we need to learn quickly is that there are games when you need to be tough, you have to be determined, to bring home the tackle, keep focused. This is part of the general growth process of some players.
“I will admit that I made mistakes on the substitutions, I got it wrong. I should’ve put more defensive players on and put the 1-0 lead under lock and key, so I take responsibility for that.”
Juventus will now target a first win when they travel to Spezia on September 22.