A dour struggle was settled by a header from Spurs sub Lucas Moura, as Burnley missed out on a first cup quarter-final since 2009.
Against a Spurs side finding their feet under Nuno Espirito Santo, did Dyche feel it was a missed opportunity?: "It is not a missed opportunity when you are playing Tottenham.
"They are a good outfit, they didn't find many moments which was pleasing
"It is about delivering performances that can win, there were a lot of good things
"I thought the fans were terrific and stayed behind the team
"In the last 10-15 minutes we were on the front foot, a couple of near misses from set pieces, and a couple of blocks from them and they got through the tie.
"The challenge is trying to turn these performances into wins."
Having gone into Saturday's game at Southampton sixth in the Premier League in terms of big chance creation, and scoring twice at St Mary's, the Clarets struggled to create against Spurs, with their first shot coming five minutes from time through substitute Ashley Barnes: "We are searching for different ways to operate.
"Talking about service, creatively before the last game we were sixth in the table for quality chances so we are obviously servicing the box with quality at times
"The magic moment needs to come our way and we have to work for it to come our way."
Nick Pope was the busier keeper, producing two fine saves on the night, particularly from Giovani Lo Celso, and Dyche feels he is back to his best: "No doubt that he is a top goalkeeper, he is back to real sharpness.
"We thought it might take a little bit of time, that is human.
"He was sharp, we gave them the chances. We have to eradicate that and the players mentioned it half-time. I asked them for a bit of feedback and they said 'we have to keep the ball with more clarity'
"We have to keep working on that but there were a lot of good things in that performance
"It is frustrating for me to keep saying it, I know how we work and I always try and call it honestly and there were a lot of good things to how we work, the energy, the commitment to the cause and I think the fans noticed that.
"They are going to be important for us."
Connor Roberts made his debut after his deadline day move from Swansea City, and Dyche said: "He did fine.
"I have been trying to get him games before he came into the side but he is a fit lad and he did fine so he will continue to develop."
Wayne Hennessey was out, with Will Norris on the bench, and Dyche explained: "He hurt his ankle and it flared up so he had to have an injection to calm it down, and hopefully it will settle down quickly."