Erik ten Hag blamed bad luck for the 1-0 loss to Valencia that ended Ajax's Champions League campaign on Tuesday.
Rodrigo Moreno's 24th-minute goal and Chelsea's 2-1 win over Lille in London condemned last season's semi-finalists to third place in Group H.
Hakim Ziyech squandered a good chance to equalise and Valencia goalkeeper Jaume Domenech made two saves at the death, leaving Ten Hag convinced a "miracle" had taken place in the Spanish side's favour.
Ajax finished with 10 points from six games and are now destined for the Europa League.
"In football you don't always get what you deserve. That's how I summarise this match," Ten Hag said.
"The Spanish press called it a 'miracle' that Valencia qualified, I think they're right. Luck wasn't on our side this Champions League group stage and luck wasn't on our side tonight either.
"Nevertheless, we got 10 points and played some good football. We did that tonight too. But on this big stage we made one mistake that led to the goal.
"After that we did create some chances, but we weren't efficient enough to finish them. Now we're left empty-handed. We did reach our personal goal, to play European football in 2020 too, but we wanted and we should have done that in the Champions League.
"That we're now knocked out is a very big disappointment."
Ten Hag described the setback as a different feeling to the heartbreak of last season, when their thrilling run came to a dramatic end at the hands of Tottenham.
"I do see comparisons with last year, but the feeling is different," he said.
"Last year, being knocked out was much more intense, because we were so close to the final. The league game after that, we could crown ourselves champions. So that explains the difference in emotion.
"But it's very clear that it's a big blow for everybody in the dressing room. Everyone's very disappointed. But we also know that we have a huge league game coming up on Sunday [against AZ]."