The England flanker was treated on the pitch for six minutes after attempting to stop Nick Easter's try, which had helped Quins into a 23-10 lead.
But 23 points from the boot of Toby Flood, along with two tries from Thomas Waldrom and a touchdown each from Steve Mafi and Alesana Tuilagi, allowed the Tigers to come away with maximum points against the Aviva Premiership leaders.
They were granted a further slice of good news after Croft was given the all-clear and Cockerill was quick to praise his squad's strength in depth.
"Tom's gone to hospital, his neck's been cleared, just a sore shoulder because he caught it at the extremes," he said.
"But you saw the strength on the squad with Steve Mafi coming off the bench, if we need to look after Tom we will. If he's fit and stops missing tackles he might get a game!
"Quins are a good side. They outplayed us for parts of the game and we struggled to contain that.
"But over 80 minutes we knew if we kept up our composure we would have opportunities to score tries and get back into the game. I was pleased with our patience.
"Sometimes when you have got lads who just want to play they're not patient and they force the game and you get yourselves further in trouble, but they had patience and kept playing and doing the little bits right according to our game plan."
After Waldrom's early score for Leicester, Quins hit back with tries from Ugo Monye - who intercepted Flood's pass - and Easter to open up a 13-point lead.
Leicester narrowed that deficit to 26-23 at the break, but even though George Lowe crossed soon after the interval, Leicester proved irresistible in the second half to leave Quins director of rugby Conor O'Shea with plenty to ponder ahead of the Premiership play-offs.
"That was a tough physical, bruising game," he said. "I think both sides felt that they are on a great run but margins in games are so small and they took them and we didn't.
"We'll review it but I'm pretty excited at hopefully seeing them again, but we've got a lot of work to do before that.
"I'm disappointed for the boys and disappointed for the crowd but the better side won on the day.
"We didn't come out of the stoppage to Crofty quite at the same level as we had gone into it. They did and they scored 10 points that was huge to the game with the try on half-time.
"We have everything in our own hands. We know what we need to do when we go up to Sale. It will be an exciting last day of the season.
"We'll just be focusing on what we need to do and not get too far ahead."
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