Tigers claimed two penalty tries from close-range scrums in the second half, including one in the 80th minute, to secure a 19-14 victory which took them to the top of the Aviva Premiership table for the first time this season.
Scott Hamilton scored the other try just before half-time as Tigers fought back from a 14-point deficit to record a vital victory.
“We started with Mulipola and Castro in the front row and then made the change after 50 minutes to get Marcos Ayerza and Dan Cole on,” said director of rugby Cockerill.
“We got the benefit of the first penalty try from the work those first guys had done and then bringing on two more quality props.
“I think the set-piece is important and, maybe because I was a front-rower, I think the team should be built from there. We have a group of top-quality props and they all work immensely hard on their game and that is very good for us.”
Tigers had been on the back foot in the first half as Warriors made the most of their possession to establish a 14-0 lead.
“They out-played us in the first half,” Cockerill said. “I don’t think it was us playing poorly, it was more that Worcester played exceptionally well.
“Regardless of how many changes we’d made to the team, or the different combinations in the team, Worcester were outstanding in the first half.
“If they’d won I would have shaken Richard Hill’s hand and said ‘well done’ because we would not have had any complaints. But we kept in there, we kept our composure after half-time and we got our rewards in the end.
“The Scott Hamilton try just before half-time helped us immensely and put a bit of a dent in them.
“The luck was on our side a couple of times. At the end we could have just kicked the ball out and taken the losing bonus point but, fair play to the players, they played right to the end and won the game.
“The extra three points after getting that late try are massive for us.”
Cockerill was also delighted to see Tom Croft back in first-team action after eight months out with a neck injury, while Steve Mafi, Thomas Waldrom and Mathew Tait also came back into the starting line-up after injury.