"It's been a hard couple of weeks, but I thought right across the board we were good for our win today," said director of rugby Cockerill following Saturday's 48-10 triumph over bottom-of-the-table Sharks.
"It was important we bounced back and it was a must-win game in the circumstances. But we were confident if we got our game right we would come through.
"We played as hard as we could and thankfully we got the five points."
While Saracens reclaimed top spot with a bonus-point win over London Welsh on Sunday, Harlequins lost at home to Exeter as Tigers were overwhelming Sale, and there were further changes at the top end of the table as Northampton Saints moved back into fourth place above Gloucester and Wasps.
"Everything is back in the melting point," said Cockerill.
"Our attitude to play was really good. In the first 20 minutes we had opportunities where it looked harder not to score than to actually score and we probably could have put the game away a lot earlier. But the guys kept going, scored some good tries and we came through with five points.
"Those points are massive for us. I'm delighted for the guys.
"We've taken 11 points from four games in this period, which is not brilliant but it gets is into the mix again with those international guys and some injured players to come back in."
Tigers go to Exeter on Saturday, March 23 (5pm) in their next Aviva Premiership fixture.