Ajax have returned home with a crucial away goal nonetheless.
Even with a first Champions League final in 23 years in sight, Ajax has some regrets.
The way Ajax overpowered Tottenham at the start of their Champions League semi-final on Tuesday left the visitors feeling frustrated to only have a slender 1-0 advantage from the first leg, secured by Donny van de Beek's first-half goal.
"In the first 20 minutes we played really good," the 22-year-old midfielder said, "and after that Tottenham chased something."
Tottenham did chase in the second half, but with a side depleted by injuries and suspension it lacked the attacking end product to equalize.
"For the first 20 minutes of the game we were just ball watchers," Tottenham midfielder Christian Eriksen said. "We made them look a look better. They are a good side but we gave them the feeling they can control things."
The Dutch side was given too much space to string together slick passes early on, and Van de Beek ghosted into the penalty area to receive a throughball from Hakim Ziyech before knocking a shot past goalkeeper Hugo Lloris in the 15th minute.
"We were completely dominating," Ajax coach Erik ten Hag said. "Tottenham changed the system (to a back four), switched to a different gear and we weren't anticipating."
Tottenham, contesting their first European Cup semifinal in 57 years, was without injured striker Harry Kane the suspended Son Heung-min. It also had to contend with the loss of defender Jan Vertonghen in the first half with an injury that threw a fresh spotlight on soccer's handling of suspected concussions.
Vertonghen challenged for a header in the Ajax area but slammed his face into the back of teammate Toby Alderweireld's head, leaving him with blood pouring from a cut on his nose in the 32nd minute.
"With a head injury it can be dangerous," Ten Hag said on beIN Sports. "Take him off. Don't take risks with head injuries."
But Vertonghen received treatment on the field and went to change his bloodied white jersey. Referee Antonio Mateu Lahoz was pointing at his head as he spoke to Vertonghen, before allowing him to return to action in the 38th minute.
Vertonghen lasted only 40 seconds before going across to the sideline, leaning over and struggling to stand. Tottenham manager Mauricio Pochettino had to grab Vertonghen to stop him from keeling over before the Belgian was helped down the tunnel by two medical officials.
"At this moment you are focused on the game, it is too difficult to think too much," Pochettino said. "Only I need to listen and hear what (the medics) say and take a decision. I am never going to debate and put into question the decision of the medical staff."
With midfielder Moussa Sissoko on for Vertonghen, Tottenham did look more assertive as Ajax's attacking rhythm was disrupted.
"We started to show more energy," Pochettino said.
But the visitors, who contest the Dutch final against Willem II on Sunday before the second leg next Wednesday, were only denied a healthier advantage when the post denied David Neres late on.
Ajax has made a remarkable advance to the last four with a youthful squad despite the Dutch league lacking the vast television revenue of the Premier League — and having to go through three qualifying rounds just to enter the group stage in September.
Tottenham is paying for investing in building a new stadium rather than its squad, making no additions this season. It's also in a scrap just to hold on to third place to take one of the Premier League's four Champions League slots.
"My players are heroes to be in the situation we are today," Pochettino said. "In the first half an hour it wasn't the best. We are still alive in the tie."
