Gloucester came into the game on the back of a win over league leaders Harlequins last weekend and another victory could have taken them level on points with Tigers as the season approaches its home stretch.
But, despite leading 3-0 early on, they were never allowed an opportunity and Tigers took the bonus-point victory to move into third place in the table.
Director of rugby Cockerill said: “We always come out fighting when we most have to. The players have been fantastic and the whole squad take huge credit for the performance.
“It was a good old-fashioned miserable day and the boys were on fire. I’m delighted with the attitude and the performance. It was a really good result, a really good performance and it puts us a little bit further ahead of the chasing pack.”
Harlequins top the table on 58 points, followed by Saracens (54), Tigers on 50 and Northampton (47), with Exeter (45) and Gloucester (41) leading the chasing pack with just five rounds of the regular Aviva Premiership season remaining.
“We needed to win today because it’s very tight in those top positions chasing a semi-final place,” said Cockerill.
“Typical Leicester, we have to wait until our backs are against the wall before we play our best stuff and we have done that since the disappointment of the defeat at Exeter.”
The Exeter game is now Leicester’s only defeat in 11 league games, but Cockerill knew it would not be easy against a Gloucester side with play-off ambitions of their own.
“There was a strong wind in the first half and we just wanted to be in front at half-time, by any score,” he said, though by that stage tries by Logoviii Mulipola, Steve Mafi and ben Youngs had given Tigers a 22-3 advantage. Matt smith and Alesana Tuiagi added further scores in the second period to take Tigers to victory.
“We will certainly take the five tries in those conditions,” he said. “And we defended well against a team that can cause problems. We were really disappointed to concede two tries against Newcastle last week and today our defence even when we were comfortably ahead was really good.