The Rossoneri believes his team should have triumphed in Amsterdam - even though they only earned a point thanks to an injury-time penalty from Mario Balotelli
The Rossoneri appeared set for defeat when defender Stefano Denswil headed the hosts into the lead as he rose highest to meet Lasse Schone's corner in the 90th minute.
|50/1||Milan are 50/1 with Paddy Power to win the Champions League this season
Still, Allegri felt his side deserved more from the game, and bemoaned the manner in which they conceded.
"We tried to slow the game down and we defended well in the first 45 minutes," the coach told reporters after the game.
"In the second half, Ajax could not keep the same level of performance. We started to play better and we should have won the game.
"Unfortunately we conceded a cheap goal on a corner and now we must feel satisfied with the draw."
Allegri reserved praise for goalscorer Balotelli, though, who went close earlier in the game when he had a curling effort tipped on to the crossbar by Ajax keeper Jasper Cillessen.
"Balotelli played well," the 46-year-old added. "He went close when he hit the bar with a great shot. He is a very important player for us."