But Carlisle, who had a hand in both goals the home side conceded, went some way towards making amends when he bravely headed home just before the break.
The Clarets, who have come from behind so often this season, pulled level from the penalty spot through veteran Graham Alexander before Steven Thompson and Jay Rodriguez ensured the three points for the home side with late goals.
The win moves Burnley up to sixth in the table and a delighted Coyle was particularly impressed with his side's fighting spirit after their energy-sapping cup season was ended at Arsenal on the weekend.
"It's game 49, we were 2-0 down and after everything we've done in the cup and coming off a massive game at the Emirates on Sunday it would have been really easy to hide yourself away and just roll over," he said.
"But those lads wouldn't allow it and we kept going right to the end and got back in it.
"I think when all said and done I felt so aggrieved to be 2-0 down. Two mistakes we're not getting away from that.
"Even in the build up to their second goal, we should have done better and they had a bit of luck and Clarke deflected the ball into his own net."
All four of Burnley's goals were fine finishes and Coyle was quick to point out his side's attacking options stand the side in good stead for the remaining nine games.
"Unlike us it was a really scrappy goal and Clarke was very brave to put himself in there and I said at half time we'd be really disappointed if we didn't win the game, never mind drawing the match," he said.
"At 2-2 Steven Thompson's goal was a tremendous individual goal and young Jay Rodriguez - it was such an accomplished finish."
Palace boss Neil Warnock was remarkably upbeat after watching his side throw away a two-goal lead and even insisted on watching the penalty shoot-out between Arsenal and Roma before speaking to the press.
He said: "After the penalty went in, there was only going to be one team who won it. It knocked the stuffing out of us and we've got to show more.
"We're not anywhere near, we know we need surgery in the summer, but tonight answered a few questions for me.
"But it's all good for me but it's disappointing for us at the moment.
"We were positive going forward but I can't really tell you what we need because it's for family newspapers."