Ben Wilkinson's youngsters couldn't recover after a first-half double blow in the form of Jahmai Simpson-Pusey's red card and Jamie Donley's deflected goal for Tottenham.
The ten-men showed courage, endeavour and determination in the second-half but couldn't find the goal to force extra time, resulting in us bowing out of the competition.
Wilkinson's side made a strong start to the encounter at the Academy Stadium, dominating the possession, however, the first big chance of the game fell to the visitors.
City failed to clear from a corner and Jamie Donley's goal-bound strike from six yards was destined for the net, but it was cleared off the line expertly by Max Aleyne.
We hit back and after a well-worked move from defence, Nico O'Reilly struck a first-time effort from ten yards, but the ball sailed over the bar.
Donley was proving to be a nuisance and just after the 25 minute mark, he was slipped through on goal but his effort rolled just wide of the right post.
It was an end-to-end game, with City coming closest next, as Ashton Muir curled over the bar in quick succession.
The match was turned on its head on the half-hour mark, as Simpson-Pusey was shown his second yellow card after an earlier offence, condemning us to ten men for the remainder of the game.
The dismissal was a boost for the visitors, who made the extra man count in first-half stoppage time, taking the lead after a corner was flicked on by Donley, before diverting into the net off a City defender, with the goal being awarded to the Spurs striker.
We emerged from the interval with an attacking intent and almost immediately equalised, but Isaiah Dada-Mascoll's attempted header hit his shoulder and went harmlessly wide.
With 20 minutes remaining, it was Dada-Mascoll again who came close to levelling the score, as his 25-yard low free-kick was deflected just wide of the post.
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We continued to push forward and it was Will Dickson to strike at goal next, but his half-volley flew off target.
We pushed and probed for the leveller, but the visitors remained rigid to cling on and advance into the semi-finals.
WHAT IT MEANS
We're eliminated from the competition after the quarter final defeat.
HOW WE LINED UP
Ben Wilkinson started with True Grant between the sticks.
He was selected behind a defence comprised of Lakyle Samuel, Jahmai Simpson-Pusey, Max Alleyne and Kane Taylor from the start.
Isaiah Dada-Mascoll sat deep in midfield, with Matty Whittingham and skipper Nico O'Reilly chosen as the more attack-minded of the midfield trio.
Farid Alfa-Ruprecht filled in on the wing, with skipper Will Dickson chosen up front and Ashton Muir on the left.
City XI: Grant, Samuel, Simpson-Pusey, Alleyne, Taylor (Galvez 65'), Dada-Mascoll, Alfa-Ruprecht, O’Reilly © (Okeke 39'), Dickson, Whittingham (Oboavwoduo 65'), Muir (Wright 34')
Unused sub: Murray-Jones.
Tottenham XI: Gunter ©, Mcknight, Linton, Dorrington, Chaplin, Abbott, Williams, Kyerematen, Donley, Olusesi, Moore
Unused subs: Krasniqi, Andiyapan, Willhoft-King, Ajayi, Lankshear
Attention quickly turns to the FA Youth Cup, as Ben Wilkinson’s youngsters host Fleetwood Town in the fifth round on Tuesday 7 February, with kick-off scheduled for 19:00 GMT (7pm UK).
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