Demy de Zeeuw and Toby Alderweireld scored second-half goals Wednesday to give Ajax a 2-0 win over AC Milan in their last Champions League group match and secure a spot in the second-tier Europa League competition.
Milan had already clinched a spot in the knockout phase, while the Dutch team finished third in Group G with seven points.
Milan finished second with eight, behind Real Madrid with 16. Auxerre finished last with three.
"It is a shame that we are in the Europa League," Ajax coach Frank De Boer said. "We were better than Auxerre and drew with Milan at home, but it is a lesson to our players that in the Champions League we have to concentrate in every game."
Ajax was the stronger team throughout the match and tested Milan goalkeeper Marco Amelia in both halves.
Eventually De Zeeuw opened the scoring in the 57th, while Alderweireld grabbed the second in the 66th.
Former Ajax striker Zlatan Ibrahimovic came off the bench for Milan, but failed to inspire a lackluster attack.
"Ajax had to show the courage to take the game to Milan and that's what we did," De Boer said. "The team was positive and we showed our true ability.
"The players followed the instructions and moved the ball from the back to the front, which was what I wanted to see. We held on to the ball well and I should congratulate the players for this, but they are an intelligent group."
The win gives Ajax caretaker coach De Boer a victory in his first match since stepping in after Martin Jol resigned on Monday.
"If it is possible, I would like the job. But I won't decide that - our results will," De Boer said. "I am giving all my energy to helping Ajax and then we'll see."
Ajax was quickly into its stride and in the second minute Amelia denied Luis Suarez the opening goal with a low save at the near post.
Amelia again stopped Ajax in the 11th when he pushed Miralem Sulejmani's shot away for a corner after the striker had cut in from the right wing.
Christian Eriksen then went close for the visitors. He turned and shot from the edge of the area but Amelia pushed his effort over bar with an acrobatic save.
Ajax continued to press, but Suarez was booked in the 35th for diving in the area and is now suspended for Ajax's next European game.
Milan finally had an effort on target in the 37th. Robinho picked out Ronaldinho with a cross from the right, but Ajax goalkeeper Maarten Stekelenburg held his header.
"We reached our objectives before tonight and we had only had one objective this evening: to play well and not lose at home," Milan coach Massimo Allegri said. "We needed much more motivation and that was obvious from the way we played."
At the start of the second half Ajax again began the stronger, but a minute in Sulejmani became the second player to be booked for diving, as he rounded Amelia.
Both sides went close from corners. First Amelia punched away Eyong Enoh's clipped shot and then Thiago Silva headed over from Andrea Pirlo's outswinger.
Ajax took the lead after Mario Yepes blocked Suarez's shot on the edge of the area. The ball ran free and de Zeeuw shot low into the corner of the goal.
Ibrahimovic came on for Massimo Ambrosini in an attempt to bring life to Milan's attack, but it was Ajax who found the net.
Suarez cut in off the left wing, laid the ball off to Alderweireld and he thumped the ball past Amelia from outside the area.
"Tonight wasn't a test for us, but if we needed a result we would definitely have got it," Allegri said. "I'm sorry about the way we played."
