Following their Champions League stalemate on Tuesday evening, the Rossoneri boss conceded that the result was a small improvement for his side
Despite a poor performance in the first half that saw the visitors dominate possession, Milan improved after the break and created several good chances, which made a draw a seemingly fair scoreline.
"I'd say we made a lot of technical mistakes in the first half," admitted Allegri, speaking to reporters.
"It's not an easy moment and, of course, the pressure is on to win every game.
"We must continue working and improving on those aspects that need improving. I think getting tense and talking too much would not be helpful.
"My lads played with effort, courage and intensity, while Anderlecht never had a shot on target. It is a small step forward, as we kept a clean sheet, so now we've got to score against Udinese," he reasoned.
Allegri did concede that injuries potentially hurt his side's chances to win, as Alexandre Pato, Robinho and Riccardo Montolivo missed the group opener.
"It's only normal that Montolivo is the player who can give us more quality in midfield, while Robinho can get past his man.
"We are missing the three most quality-led players in the squad, so of course that's going to change the way we approach the game."
The Milan boss was keen to look towards his next fixture in Serie A, against Udinese.
"Montolivo will return on Saturday, and everything does not have to be thrown in the bin. It is a growth process and we've got to speed it up."