Former Tigers wing Tom Varndell scored the only try of a rain-affected game which Wasps won 14-12 to preserve their winning home record this season.
George Ford kicked four penalties for Tigers who headed home with just a losing bonus point as consolation.
“It was a disappointing game all round,” said Tigers director of rugby Cockerill.
“We didn’t get any field position or control, we didn’t get the ball to play with and we struggled to get on the front foot all afternoon.
“They pushed in behind us in the second half and we found it hard to get out.”
Tigers were without 10 senior players on international duty, but Cockerill said: “We have guys away and a few injuries but that is not an excuse because it does a dis-service to the guys in the dressing room. Those guys are disappointed because they obviously wanted to win the game.
“It’s a tough environment in the Aviva Premiership, it is very unforgiving, but now we have turn around and pick ourselves up and be ready to face Bath at home next weekend.”
Martin Castrogiovanni, Marcos Ayerza, Steve Mafi and Vereniki Goneva are all due to return to training with Tigers this week at the end of their international programme and will be in contention for Saturday’s game.
Kick-off against Bath is at 12.30pm on Saturday and tickets are available now.
