The visitors were without leading scorer Charlie Austin, who had his appendix removed in the morning, and Rudy Austin scored the solitary goal for Leeds.
Burnley have won only two of their last 15 league games and lie just three points above the relegation zone.
"They were the better side," said Dyche. "Apart from a little rally at the end, they were better.
"They showed their experience and that's interesting because the same group of players weren't playing like that two weeks ago because I saw them.
"So that's an interesting one in itself, but we caught them on a night when they were on the front foot and we weren't quite at it.
"There wasn't that freedom in our play tonight, there wasn't that 'front-foot thinking"'.
Dyche is refusing to panic, despite his side's precarious position, and hopes his side can get back on track against promoted Cardiff on Saturday.
"It's the same plan as always, to win as many games as you can, nothing's changed," he said.
"We're not naive, we'll make sure we're looking over our shoulder to see what the market is telling us and that's to get points on the table.
"But it's telling a lot of other clubs that as well. It's the maddest year we've ever had."