They will hope to reach the last eight of the competition by travelling via Lisbon next week, although they will be required to overcome a 3-1 deficit from the first leg before they will be able to continue on their way.
The defeat by Benfica last night bruised Spurs. They were a side already nursing the wounds of a 4-0 loss to city rivals Chelsea and the cutting criticism of head coach Tim Sherwood.
He had reacted furiously to that defeat at Stamford Bridge and Sherwood would raise his voice again last night as Tottenham fell behind within the opening half hour as Rodrigo struck.
The Portuguese side were always likely to provide stern opposition since they have not been beaten in 18 weeks. They had scored their second goal last night within 13 minutes of the second half as Luisao headed in.
Christian Eriksen responded for Spurs but the two-goal cushion was restored by Luisao with just seven minutes remaining. It sparked an ugly altercation between Sherwood and his Benfica counterpart Jorge Jesus, with both men refusing to shake hands at full-time.