Michael Kightly struck the only goal of the game as the Clarets moved back to the summit of the Championship this afternoon, with Leicester City and Queens Park Rangers both failing to secure victories.
However, the win over the Tykes signified the end of a five-game winless streak for Dyche's men in England's second division, but the 42-year-old does not believe that the team's recent form constituted a "crisis".
Speaking to reporters, the coach said: "I've read this week that we've been going through a mini-slump.
"Well, we've dropped from the top to third place and then back to the top, I hardly see that as a crisis.
The former Watford boss went on to claim that his side are more than a match for any team in the Championship.
He added: "I gave the players a bit of a reminder just how good they are at half time, and that's clearly had a positive effect.
"On our day we can match anyone in this division. We just needed to work out a way to win the second half, and we got there in the end."
Burnley could extend their lead over the Foxes at the summit of the division to four points next week when they travel to the King Power Stadium.