Ajax needed points to be sure of Europa League qualification and poured forward for the 2-0 victory at San Siro.
"Behind this result is the lack of motivation, but that doesn't mean playing like this," moaned the Coach.
"We should not have put in a performance like that, it should've been different. Now we have to start again and on Sunday there is an important match against Bologna."
Mathieu Flamini limped off with a knee problem in the opening stages, while Ronaldinho wasted his first start in eight games.
"It's a shame about Flamini, as he almost certainly won't be fit for Sunday," continued Allegri.
"Ronaldinho played and did some good things, some not so good. When the team plays like this it's difficult for any individuals to stand out.
"Towards the end he did set up some good chances for Zlatan Ibrahimovic and Robinho. If we do sign a centre-forward in January, it has to be someone worthy of Milan."