The Rossoneri trailed 1-0 in the 89th minute after Stefano Denswil had put the Dutch giants ahead but the Italians hit back with Mario Balotelli equalising after earning and converting a penalty deep into stoppage time.
"I am very happy with what my team has done," Allegri said on acmilan.com. "My team played great in the second half and just when we were playing at our best they scored.
"We risked losing a game that we didn't deserve to lose. But we didn't give up and we were rewarded."
The result has lifted Milan to second in Group H, two points behind leaders Barcelona and three clear of third-placed Ajax.
"This is an important point in view of progressing to the next round," Allegri said.
"Of course, we could have won considering the chances we had and taken six points which would have put us on the verge of qualification.
"But to have taken four points in the first two games is a good result."
Milan host Barcelona on October 22.