Spurs enjoyed their best spell early in the second period as they switched to a more direct approach and Dele Alli had a couple of half chances.
An improved home side looked to push forward in the second 45 minutes but their lack of final third ability was evident in the absence of Harry Kane and Son Heung-Min.
Temporarily, Ajax lost their composure as Tottenham pressed for an equalizer in front of the huge, new one-tiered stand housing their most vocal supporters.
Pochettino turned to Fernando Llorente and Lucas Moura to spearhead his attack, going with three former Ajax products in his defense and Danny Rose and Kieran Trippier at the wingback positions to account for who he did and did not have available for selection.
The goal survived a VAR check for offside and it was nearly two eight minutes later but another picturebook move, which saw Dusan Tadic play Van De Beek in, was thwarted by the legs of Lloris. But they couldn't find a momentum-changing equalizer despite a few decent looks at goal.
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.
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"No one wanted to play the first half we did".
'We're lucky they hit the post and hopefully we can turn things around in Amsterdam'.
It was how they dominated the previous two second legs, at the Bernabeu and in Turin, as they saw off the holders and favourites en route to the semi-finals.
Hakim Ziyech slipped the ball through for Donny van de Beek, who controlled the pass and converted past Hugo Lloris after taking some time to compose himself.
There was no need for a VAR check as replays showed the midfielder was marginally onside and Ajax kept their foot on the accelerator, with Rose nearly slicing into his own net and Van de Beek being denied by Lloris at his near post following a fine dummy.
Domestic cup competitions haven't gone well for Spurs by any stretch, crashing out of the FA Cup to London rivals Crystal Palace in the fourth round and having a firstleg semi-final in the League Cup overturned by Chelsea - both results in the space of three days at the end of January.
At 1-0, the final score was deceiving. We won the game.
The introduction of midfield powerhouse Sissoko injected some much-needed energy into a flagging Tottenham side and he fizzed a shot wide from Llorente's knockdown before halftime.