Ajax through Donny van de Beek scored the only goal of the game to give the Dutch side the advantage heading into the second leg of the semi-finals.
It was a fine performance from Ajax, whose young stars played some wonderful football at times and did a solid job defensively, especially in the second half.
Harry Kane (injured) and Son Heung-min (suspended) were both missing for Spurs and their absence was felt going forward.
Just like they have all season, Ajax made a blistering start to the first half as they dominated Tottenham and created several chances.
And in the 15th minute, the Dutch side’s dominance paid dividends.
A lovely passing move saw Hakim Ziyech put Van de Beek through on goal with an inch-perfect through ball. Van de Beek had all the time in the world and made no mistake.
Nine minutes later the 22-year-old could have made it 2-0 but he shot straight at Hugo Lloris instead of squaring to a teammate.
As the game progressed Spurs slowly improved, with Fernando Llorente and Toby Alderweireld both meeting free-kicks from Kieran Tripper but heading off target.
One concern for Pochettino was the injury to Jan Vertonghen, who suffered a suspected broken nose after a collision with Alderweireld and was unable to continue.
Spurs came out much stronger in the second period and both sides had chances to score in a frantic opening five minutes.
Moussa Sissoko’s introduction in place of Vertonghen had a big impact, with the Frenchman’s pace and power helping to handle Ajax’s midfield.
But in the final third there just wasn’t enough from Tottenham. Lucas Moura had a quiet night, while Llorente and Dele Alli had opportunities to score but didn’t take them.
Spurs almost went 2-0 down in the 78th minute when David Neres’ shot looked to be heading for the bottom corner, but it hit the post.
One-nil was how it ended and Ajax’s players will be very confident of seeing out the tie at home next week.