"We were under the cosh for long periods of time, but the boys dug in," Cockerill said after Tigers added a second win following the opening-day 26-13 verdict at Bristol.
"We have got some great players across the board but we were flat, we did not do the simple things well and did not play how we practised.
"Across the park we were a bit lacklustre, but the spirit was great, I cannot fault the guys' commitment. We dug out a win and four points is four points."
Cockerill would have been delighted with eye-catching tries from full-back Johne Murphy and winger Matt Smith, who made his first Guinness Premiership start after injury to Ayoola Erinle at Bristol.
Scotland U-21 international prop Dave Young also gained some useful experience after replacing Julian White in the opening minutes of the match.
"Julian White got a bang from a collapsed scrum," said Cockerill. "Dave Young came in and stood up well, he did a good job. This is a good testing ground."
Cockerill spared a thought for opposite number Steve Meehan, the Bath head coach.
"To be fair, if I was them I would he hugely disappointed not to get anything out of the game," said Cockerill. "But I will take the four points because on another day perhaps the luck does not go in your favour."