Cockerill felt the Tigers were harshly penalised throughout the top-of-the-table clash, which Quins won 25-21, and suffered at the hands of some inconsistent officiating from Barnes.
"The discipline was disappointing in the game for us. Some of that was ourselves and some was down to the officiating, which at times was disappointing," said Cockerill. "I thought we were getting penalised for certain things and then I thought the opposition did the same thing but they weren't."
Toby Flood registered 16 points for Leicester on his return to Premiership action, while Adam Thompstone touched down for the Tigers, but it was not enough for the visitors as Care scored a scintillating long-range effort for Quins and Ben Botica added 20 points with the boot.
"I thought it was a half-decent game of rugby and it was tight, but they take the win and we take a point," Cockerill added. "We have Saracens at home next week and so it's not all lost and we now need to regroup and just carry on.
Meanwhile, Quins boss Conor O'Shea hailed the performance of Care, calling the number nine the difference between the two sides.
"The right reaction was to come back and perform for your club. That was world class out there. You're fortunate to be able to watch those types of moments," O'Shea said.
"From Stuart Lancaster's point of view, he must be thinking, 'I've got Ben Youngs and Danny Care - how lucky am I?'
"From my point of view, we love having him back. He got stuck and got physical; looking at the team we were physical we were magnificent.
"I'm always going to back my own player. Danny's outstanding. From Stuart Lancaster's point of view there are two Lions-standard scrum-halves competing."