Luke Varney and Ross McCormack had the Whites two goals to the good by the 50th minute before Clint Dempsey gave Spurs some hope with a response just before the hour-mark at Elland Road.
But Neil Warnock’s Leeds held out for a famous victory which sees them move into the fifth round where they will meet Manchester City and their showing was praised by Villas-Boas who felt it was a tough day for his Tottenham team.
"It was difficult," said Villas-Boas. "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 today, and you have to give credit to them."