Allegri thinks Milan could've won against Barcelona had they been sharper on the counter-attack after their amazing start.
"The team did very well at the start, then we got a bit too deep, mainly because of Barcelona's pressure. We could've done better with some counters and keeping possession, but it wasn't easy," he said after the 2-2 draw.
"I don't think we allowed Barca many chances and could've gone 2-0 up straight after the opener."
Alexandre Pato scored after 24 seconds, making it the fifth fastest goal in Champions League history.
"The lads did well not to lose their heads after going behind and were rewarded for all the hard work and sacrifice they did over the 95 minutes," continued Allegri.
"I didn't expect this, as it's not easy to come here and score twice. We all realised it was difficult and held firm, as Barcelona are capable of scoring three goals in five minutes."