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Ainsworth thought his side should have had two penalties in the second half and said after the game: "I thought Dexter Blackstock was out muscled for the first one. Clarke Carlisle's got back well and got his body in the way, but I think the second one is a stone-wall penalty every day of the week.
"I've seen the tape back and the ball moving forward, Dexter got taken down and in my opinion that's a penalty. I think the referee got it very wrong and there were a few decisions that he got wrong for both teams.
"I'm gutted for the boys. They worked really hard. We weren't at full tilt and there were a few players under par, but I can't fault their efforts.
"But for me the whole game changed on the referee's decision not to award the penalty at such a crucial stage of the game."
Winning manager Owen Coyle spoke about his players and their desire to do well for the club, after seeing them end a week on the road with a second victory out of three.
"With Wolves away, Chelsea away and QPR away it was going to be a daunting task, but all credit to the players because they have shown the desire they have to play for the football club.
"It was going to be a big ask today, given the exertions of the midweek win, but I thought we started the game well and actually felt a bit aggrieved to be a goal down. But the spirit and the desire the lads have for each other was so evident, and it was there in abundance.
"To come back, after everything we've done during the week, just shows the strength of character we have to go with the ability."
Burnley came back from behind to level with a goal from Robbie Blake and Coyle added: "We'd threatened to score before that and I thought some of our passing and movement was pleasing on the eye. But when you're doing all that you have to have a cutting edge, and Robbie showed that.
"We took enormous belief from that, and in the last fifteen minutes of the first half there were waves of attack and the precise passing was really pleasing with the level and tempo we played at. And I was delighted to go on and win the game in the second half.
"Away from home there are always going to be spells where you have to deal with pressure, and QPR had that. They had two or three appeals for a penalty and I've seen days when they've been given. But it wasn't and I think we thoroughly deserved the three points over the piece."
In the last two games both Ade Akinbiyi and Alan Mahon have followed Robbie Blake back into the first team and there were words of praise for them from Coyle. "I've got nothing but praise for the likes of Robbie, Alan and Ade, particularly Alan and Ade this last week, because they've been out of the sixteen for the last seven or eight games.
"I brought them into the fold for the cup tie during the week, they've been working their socks off at training, and I felt that it was earned and deserved.
"I've said before, sometimes you get luck with your substitutions. Chris Eagles had taken an injury and we felt Alan was the proper replacement at the time. He scored a wonderful goal and then we had to reshuffle again.
"But no matter what you ask of those lads, if you ask them to play out of position, or sometimes to play not 100 per cent fit, I know they're going to give their all for me and I can't ask any more than that."