Ajax manager Erik ten Hag felt Liverpool was "vulnerable" against his side as he rued the Dutch giant's bad luck in the 1-0 Champions League loss.
Ajax had its chances but Nicolas Tagliafico's first-half own goal was enough for Jurgen Klopp's Liverpool in the Group D clash in Amsterdam.
Liverpool was winless in three games heading into the encounter, and in action for the first time since Virgil van Dijk suffered a serious knee injury in the Premier League on Sunday (AEDT).
Ten Hag said he felt the Eredivisie glamour club could have taken advantage of the Premier League champion.
"It would have been a big bonus if we had taken one or more points," he said. "I think Liverpool was vulnerable. Unfortunately, we didn't make the most of that.
"We were unlucky. We performed well collectively. We were convincing, but that last one per cent was missing – we didn't score even though we created many chances.
"That's the story of this game, I think."
Tagliafico turned in a miscued Sadio Mane effort 10 minutes before half-time for the game's only goal.
Ten Hag said there were elements of Ajax's performance he was pleased with.
"We knew Liverpool's strength, we wanted to prevent their full-backs, who are their playmakers, from going forward. That was one," he said.
"The second thing is that we wanted to control the midfield. Daley [Blind] is very good at that, he's so calm on the ball. And in that way, we wanted to attack their defence with deep runs. I think we did that quite well a couple of times."
While Trent Alexander-Arnold had a quieter performance for Liverpool, left-back Andy Robertson impressed.
Robertson had the most key passes (five), passes (78), passes in the opposition half (56) and touches (104) of any player on the ground.