Leeds striker Luke Varney held his nerve after being sent clear by skipper Michael Brown's throughball in the 15th minute to open the scoring, and Spurs' hopes of a fightback were dealt a blow five minutes after the break when Ross McCormack slammed home a fine second.
Clint Dempsey deftly headed Gareth Bale's excellent cross inside the far post eight minutes later, having earlier spurned a gilt-edged chance to reduce the deficit, but there was no way back for the Londoners.
"It was difficult," said Villas-Boas, who made five changes to his side. "At 2-0 Leeds got further inspiration and we wanted to get back quickly.
"We had a good 15 minutes before the goal when we had some good chances, and I think it was important to score early.
"It was difficult as we were always chasing the game and this is a difficult place to play, and we couldn't play our football as well as we could have.
"We wanted to go through in the competition, but we were knocked out by a Leeds team who were extremely competitive, and you have to give credit to them."
Tottenham were without Emmanuel Adebayor, on duty for Togo in the African Nations Cup, while Villas-Boas confirmed absent striker Jermain Defoe had injured himself in training.
But the Spurs boss refused to comment on whether he would be drafting in any forward cover in the final week of the transfer window, and did not accept his side would benefit from this defeat in terms of their bid for Champions League qualification.
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