David Nugent's 12th goal of the season was enough to see off the hosts, who had already received a hammer blow after seeing leading scorer Charlie Austin limp off after just eight minutes.
Dyche's men sensed at least a point was there for the taking, but were unable to get past Kasper Schmeichel who made second-half saves from Martin Paterson and Danny Ings.
The Clarets boss said: "We could've nicked a point but I don't think we did enough to win the game.
"We didn't use the ball well enough or keep the ball well enough. We did create some chances to be fair, but with our performance levels I think a point is the best we could've expected.
Dyche continued: "I believe in the performance levels of the players and it wasn't there in this game. We were flat in the first half and I thought the whole feel of the game was flat.
"It was a really poor goal from our point of view and we've been really good defensively since I've been here. It was a really soft one.
"We responded slightly but not with the urgency we've had lately. We weren't good enough."