Milan needed a last minute penalty from Mario Balotelli to rescue a point.
"We knew the difficulties would be in the first half, as the same happened in Eindhoven with PSV," Allegri told Sky Sport Italia.
"There was no point pushing early and risking to get caught up in their passing, so we played very well in a defensive fashion and risked very little.
"In the second half it was normal their tempo would drop and from that point on we could win the game. We lost a few balls at the end and conceded from a corner.
"It's a good point for qualification and overall I think we played well. In the first half it was tactically a good performance, while after the break we took it to Ajax.
"I think it's difficult to play 90 minutes with great intensity and constant pressing, especially when we've had a packed fixture list with few players available.
"We did make mistakes to give Ajax too much space in the first half, as we kept giving the ball away. The team wasn't spectacular, but it played the way I asked in the first half.
"The second was in our hands and we didn't have enough quality in the final pass, but overall it was a good performance. A game lasts 95 minutes generally and you have to be in front at the end."
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