Their last-eight tie against PSV finished 1-1 and therefore went to penalties and the Dutch team ran out 4-2 winners in the shoot-out.
Souleymane Coulibaly opened the scoring from the penalty spot in the 16th minute of the 50-minute match only for PSV to equalise a minute later.
Jack Munns and Laste Dombaxe were successful from the spot in the penalty shoot-out.
Spurs v PSV: Miles, Barthram, Ekong, Veljkovic, Gomelt, Dombaxe, Ball, Hawkins (Bentaleb, 35), McEvoy, Ward (Munns, 27), D McQueen (Coulibaly, 14).
QUARTER-FINAL QUALIFYING MATCH, SUNDAY
Jack Munns' goal three minutes from time beat Sparta Prague 1-0 in Sunday morning's quarter-final qualifying match.
Spurs: Miles, Barthram, Veljkovic, Ekong, Stewart, Bentaleb, Dombaxe, Munns, Coulthirst (Lameiras, 39), McEvoy (D McQueen, 48), Coulibaly.
GROUP STAGE, SATURDAY
In the group stages, goals from Nabil Bentaleb and Souleymane Coulibaly were enough to beat New York Cosmos 2-0 on Saturday but the team were then beaten 2-0 by Fortuna Dusseldorf, setting up Sunday's match against Sparta Prague.
Spurs v Fortuna: Miles, Ward, Stewart, Veljkovic, Barthram, Hawkins (Lameiras, 33), Gomelt (McEvoy, 33), Munns, D McQueen (Bentaleb, 26), Coulthirst, Coulibaly.
Spurs v New York: Miles (McGee, 42), Barthram (Ward, 48), Ekong, Ball, Stewart, Dombaxe, Bentaleb, Lameiras, McEvoy, Coulthirst (Munns, 40), Coulibaly (D McQueen, 47).