Following a bonus-point victory over the Ospreys last week, Tiger won 21-18 at Sixways to make it two out of two in the Anglo-Welsh competition.
“I’m delighted with the performance,” said Tiigers director of rugby Cockerill.
“There were some really gutsy performances from the young lads, especially after making such a poor start.”
Tigers conceded two tries in the opening 20 minutes and trailed 10-0 before three kicks from Owen Williams cut the deficit to a single point by half-time. A Michael Noone try and a penalty try from a scrum allowed Tigers to pull away before Warriors claimed a last-minute score from a lineout.
“I thought we conceded two pretty soft tries in the first half, with a defensive error for the first one and a mistake under the high ball and the bounce for the second try,” added Cockerill.
“But fair play to the lads, they did really well to come back from that. Heads could have dropped after that start but they stuck to their guns and kept to it. They believed in themselves and they got out of the hole.
“That play just before half-time when we nearly scored from the Miles Benjamin break and they got a yellow card, that gave us a bit of belief. At half-time we just said believe and do what you are doing.
“I think the longer it went on the more our belief grew.
“Across the board the young lads kept their heads and stepped up, and the senior lads did a really good job in holding it all together and we just did enough in the end to come through with the win.”
Tigers resume LV= Cup duties in the new year with a trip to Harlequins and a home fixture against Bath.
