Harry Kane opened the scoring in the 21st minute of an entertaining game at White Hart Lane, heading in Nacer Chadli's cross after a quickly-taken free-kick.
Burnley responded quickly and were level soon afterwards when Ashley Barnes shot into the top corner from just outside the area for his second goal in as many matches.
But that superb effort was usurped by Erik Lamela's first Premier League goal as the Argentinian curled an unstoppable shot beyond Tom Heaton from 25 yards.
The visitors had chances in the second half, Hugo Lloris denying Danny Ings on three occasions, but Burnley were unable to force an equaliser as they dropped back into the bottom three.
"I'm proud of that," Dyche said. "We wanted to play an effective game and we wanted to get the ball forward quicker than we have been doing.
"We felt we could affect the game with that and we did. I think Ashley Barnes and Danny Ings were sharp, we made chances and we were solid in our shape and one of the goals is a poor goal from us to concede."
Dyche felt aggrieved at the nature of Spurs' opener, which came after a free-kick had been awarded when Kane's header struck Michael Keane on the arm.
Kane quickly put the ball down and played a pass towards Christian Eriksen, who was stood in an offside position and left the ball alone. Chadli ran on to the loose ball and provided the cross for Kane to score.
"I'm a bit disappointed with the decision I've got to be honest, because Keano is behind it," Dyche said. "It takes a flick off Harry Kane and it's ball to hand for me because Michael can't do anything about that.
"Then they play a quick free-kick and we all know the debate of offside. Their lad steps out the way of it and that's got to be interfering, but it wasn't deemed so and they run through and score.
"The reason I say it's interfering is because if that's in the lines of the box then surely it is.
"I was disappointed in that moment because it cost us dearly, but other than that there were a lot of good signs again.
"I speak about the growth of the players a lot because they are improving and getting more experienced to come to this stadium and perform in that manner."
