The Cottagers grabbed their first win since returning to the Premier League. Burnley have now extended their winless streak in the competition to eight games.
And Dyche says he'll be working on his team's defending in the upcoming weeks.
"They were the better side. More inventive, more productive and possibly signs that their £100m has been spent well it seems on that performance," he told Sky Sports.
"We huffed and puffed our way back into the game, we have a spirit and a belief and demand in the players and they've at least got themselves back in it at 3-2. We had some moments, so did they, but realistically over the whole game, they were the better side.
"We conceded two sloppy goals [from Aleksander Mitrovic]. We don't normally do that, we had a couple against Watford as well, so that's something we've got to look at and tighten that side of things up. It's tough then.
"They're a good side and I was impressed with some of their football, we knew that from last season. The difference was their centre-forward [Mitrovic], I thought he was the best player on the pitch by a long shot.
"At the end of the day, our performance wasn't up to where it needs to be and theirs was."