Spurs went down 2-1 at home to 10-man PAOK Salonika on a controversial night at White Hart Lane.
The home side went two goals down, pulled a goal back and then thought they had equalised through Jermain Defoe in the second half, but referee Bas Nijhuis penalised the striker for a foul.
Tottenham now need to win against Shamrock Rovers in Ireland in a fortnight's time and hope PAOK overcome Rubin Kazan in Thessaloniki.
Birmingham missed a first-half penalty then conceded the only goal of the game shortly after the break for a 1-0 defeat at Braga.
The Blues can still qualify if they beat Maribor at home next month.
Rubin Kazan 4-1 Shamrock Rovers, GpA
Haedo Valdez Oman 12
Braga 1-0 Birmingham, GpH
FC Metalist Kharkiv 4-1 Austria Vienna, GpG
Devic 17 Mader 19
Lacerda Edmar 40
Malmo 0-0 AZ Alkmaar, GpG
NK Maribor 3-4 Club Brugge, GpH
Volas 11 , 68 Donk 90
Hoefkens og51 Dirar 74 , 77
Rennes 0-0 Udinese, GpI
Legia Warsaw 0-3 PSV Eindhoven, GpC
Zewlakow og 32
Mertens pen 60
Rapid Bucharest 1-3 Hapoel Tel-Aviv, GpC
Deac 43 Nosa Igiebor 12
Tamuz pen 40
Tottenham 1-2 PAOK Salonika, GpA
Modric pen 39 Salpingidis 6
Vorskla Poltava 1-1 FC Copenhagen, GpB
N'doye og 31 N'doye 37