The struggling hosts had much the better of the first half at Turf Moor with Danny Ings, Scott Arfield and George Boyd all going close.
Liverpool weathered the storm, and scored the winner in the 62nd minute as Raheem Sterling ran on to Philippe Coutinho's pass and produced a composed finish.
Defeat ended Burnley's four-match unbeaten streak at home, and Dyche felt his men were unfortunate to end up on the losing side.
"You can never guarantee what you should deserve from a performance," he said. "But I think it's fair to say we had our pocket pinched today with how they get away with a win. But sometimes that's how it is.
"It's a marvel really to see the strides the group has made. I thought we were excellent in the first half.
"But we know the challenge. It's not to be excellent, it's to win. We were better today than we were against Southampton [a 1-0 victory].
"To see the group playing how they did today was great. There's an assured manner in the way the players are playing.
"If we keep playing how we did there's real good signs. We probably didn't get the rub of the green.
"Sometimes you need a deflection or a bounce, that didn't quite come for us.
"There's a big future in those performances. I'm definitely encouraged. You can't be sick because we all have to do that [grind out results]. We did it at Stoke [a 2-1 win].
"But there's no naivety, we've got to win games."
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