The Lancashire club - who drew 1-1 with Spurs in the initial third-round clash last week - raced into a two-goal lead after eight minutes as Marvin Sordell opened his Burnley account with a stunning volley and Ross Wallace's deflected free-kick deceived Michel Vorm.
Burnley failed to make the most of their quick start at White Hart Lane, though, as Paulinho reduced the deficit in the 10th minute and Etienne Capoue restored parity in first-half injury time.
The hosts paved the way for a fourth-round clash with Leicester City after the break as Tom Heaton's error gifted Vlad Chiriches the third before Danny Rose rounded off the scoring in the 52nd minute.
And Dyche felt his side were punished for a series of uncharacteristic errors.
"It was a good game for the neutral," he said. "We came here to win but it was a game of mistakes from us.
"We've learnt well over the season but there were too many mistakes.
"There were a number of things that didn't go our way but we can't defend like that at key moments.
"We didn't make good decisions. Eventually if you keep making poor decisions, you get hurt."
However, Dyche was able to take some positives from the game as striker Sam Vokes played a full match for the first time since sustaining a serious knee injury last March.
He added: "The big positive is Sam Vokes coming through 90-odd minutes, because after nine months out with a serious injury that's massive for him."
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