The Clarets boss felt his men were made to rue missed chances at one end before being punished by Leeds at the other.
After a good start, in which they stopped Leeds from playing, Burnley came under some pressure and then conceded the opener, Mateusz Klich running unopposed from halfway to beat Bailey Peacock-Farrell from distance.
The second half saw Leeds move clear with a Jack Harrison flick, before two goals from substitute Rodrigo made the three points safe.
"We started well and stopped [the way Leeds want to play] occurring, allowed a goal to their liking," said Dyche.
"They get two in front and we had golden chances and you can't miss them. Leeds do concede as well as score and we shouldn't have missed those.
"Those chances could have changed the feel of the game, their keeper makes two good stops."
Dyche refused to be critical of his men, who secured Premier League status for next season with their win over Fulham last week.
"It's hard to ask a lot more of my players, we had an emotional game on Monday and big result, I was expecting us to slide off it more than what we did really, but physically we were still at it," he said.
"They were clinical, they're having a good run of form and a great season. We look like we're huffing and puffing just trying to see the season through - my players have worked hard.
"Tough games, all games are tough for different reasons. Sheffield United are adding some pride after a tough season for them after a good one last year. It's rebuilding for us, we've had awful injuries and been a bit thin on the ground but there's been no lack off effort from us, just a lack of clinical finishing. No doubt they're a good outfit Leeds."
Dyche insisted he was not being critical when he suggested a 'baseketball game' suited Leeds more.
"That's their style, it's certainly not derogatory," he said.
"They want it to be fast, active and work on turning it over. We didn't allow them to do that in the first half and the first time we did they scored a goal.
"You've got to open up to try and win the game, which we did. They were very clinical today, credit to them for that. We weren't a million miles off but we weren't as clinical as them.
"Statistically, if you take the scoreline out, it was quite a similar game for both teams. They've recently beat Man City away, their tails were up."