"I would say we deserved more than third spot," Ajax coach Frank de Boer said. "Our game is more positive. It seems to me that anti-football won today. In football the best teams don't always win but we should be proud of this squad, which is a really good one, and we shouldn't be scared of anyone.
"The red card conditioned the game but it's also true that it was deserved," he added. "When someone plays on the man rather than the ball, he deserves to be sent off. (Mario) Balotelli was also lucky not to be sent off in the second half, so Milan should be thankful they played the match in 10 men not nine."
Milan rarely threatened but managed to earn the draw it needed to qualify for the knockout stages for the 11th consecutive season.
"We were in 10 men after 20 minutes, it's normal we had to play like that," Allegri said. "Today the team defended as you should do when the other team has the ball. Tonight the other team had the ball more than us as they were 11 against 10 so we defended more. I think that's normal."
Milan needed just a point to progress and was undefeated at home in the Champions League. Ajax had not won any of its last six away fixtures in the competition but was full of confidence following a shock 2-1 defeat of Barcelona.
The visitors almost got off to the perfect start but Cristian Zapata perfectly timed his interception to clear for a corner as Viktor Fischer was about to hit Lasse Schone's cross.
Ajax went even closer from the resulting corner but Poulsen headed off the inside of the left upright.
Milan was pressing but struggling to carve out clear goalscoring opportunities, while Ajax again went close in the 19th minute with Davy Klaassen's diving header which Abbiati did well to turn around his post.
A moment of madness from Montolivo saw him shown a straight red card and left Milan with 10 men for the remaining 68 minutes.
Allegri immediately rang the changes, bringing off Italy forward Stephan El Shaarawy who was making his first start after three months out with injury and replacing him with Andrea Poli.
Milan fans, realizing how difficult the situation had become, immediately got behind the players, upping the noise levels at San Siro and resoundingly jeering every time Poulsen touched the ball.
Ajax almost made its numerical advantage count immediately but Schone was denied by another fine Abbiati save.
The Dutch side could have taken the lead on the stroke of halftime when it was awarded a free kick in a dangerous, central position after Sulley Muntari shoulder-barged over Klaassen. But Schone blasted over the crossbar.
Milan seemed to be content to camp out in its own half and try to attack on the break. Massimiliano Allegri's men did not have a single shot on target the entire second half and it almost got caught out several times, but Ajax couldn't find the finishing touch.
Abbiati pulled off another good save in the 67th minute, using his legs to block an angled drive from Klaassen, who had been left unmarked on the right side of the penalty area.
Ajax again went close to breaking the deadlock but Fischer's attempt rolled narrowly past the far post.
The visitors almost snatched a win with the last kick of the game, but substitute Kolbeinn Sigthorsson's overhead kick flew narrowly wide of the left post.
