The home side took the lead through Kevin Doyle in the first half, only for Danny Ings to equalise. Richard Dunne then scored from a corner to give the hosts a 2-1 lead at the break.
Burnley started the second half brightly and raced into a 3-2 lead thanks to a Sam Vokes double. However, the visitors couldn't maintain their lead, Modibo Maiga levelling late on.
Speaking to Sky Sports News after the game, Dyche told reporters that he was delighted with Burnley's performance: "It's a tough place to play. I thought the manner of how we went about it was impressive, the way we tried to win.
"We believe in going to win and I thought we did everything but today, and the players were terrific.
"We like to play with a tempo and shift the ball around quickly and with our forwards we have good outlets. I want our football to be mixed and try to hurt teams in as many ways as we can and I thought we did that today. Having said that we did give away some soft goals by our standards."
Burnley currently occupy third place in the Championship table.