23 points from the boot of England fly-half Toby Flood, who missed most of the RBS 6 Nations through injury, along with two tries from Thomas Waldrom and a touchdown apiece from Steve Mafi and Alesana Tuilagi allowed the Tigers to come away with maximum points against the Premiership leaders.
And Cockerill - whose side now sit a point behind Quins - believes Croft's injury is of no long-term concern.
"Tom's gone to hospital, his neck's been cleared, it's 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' scores came from Easter, George Lowe and Ugo Monye while Nick Evans kicked 18 points but it wasn't enough to stop the Tigers taking the win.
Elsewhere, the battle to avoid the drop will go down to the wire after Wasps lost 17-12 at Bath and Saracens beat Newcastle 9-3.
England's Owen Farrell kicked Sarries' nine points but it was a late penalty from Wasps No. 10 Nicky Robinson that may yet prove vital in the relegation battle.
The three points bagged the Adams Park outfit a losing bonus point, meaning the Falcons need a bonus-point win - while denying Wasps one - in their season-final showdown next weekend.
Delon Armitage was among the scorers as London Irish tasted victory for the first time in eight league games with a 25-16 win over Worcester while Sale all-but guaranteed their Heineken Cup status with a 24-19 win over Gloucester.