Goals from Luke Varney and Ross McCormack gave Leeds a commanding lead, but Clint Dempsey's goal set up a tense finale and the hosts defended stubbornly to secure a place in the fifth round.
"It's a fabulous performance," said Warnock. "It's a great day for us. The atmosphere was good, two cracking goals.
"There were a lot of heroes today. It was a typical FA Cup tie today."
Warnock was delighted with defensive duo Sam Byram and Aidy White who helped to shackle a Spurs forward line which included Gareth Bale and Aaron Lennon.
"I thought Aidy and Sam got done occasionally, but they've learned so much today against top-class opposition," he said.
"It's not very often that Aaron Lennon has an ineffective game as he did today, and we handled Gareth well as well."
Top-scorer Luciano Becchio was left out by the hosts as he is expected to leave Elland Road, but Warnock insisted his preparations had not been disrupted by the absence of the striker.
"If I'd have thought Becchio would have been fit today or in the right frame of mind I would still have played this team," he said.
"The lads knew on Wednesday I was going to play this team."