The game heralded the return of most of the Tigers' World Cup participants with Toby Flood and Manu Tuilagi starring in the win.
The Cherry and Whites pack were clearly second best, allowing Flood to control proceedings and collect a match tally of 18 points.
Cockerill admitted victory was a weight off the Tigers' shoulders and said: "It's a nice feeling to get that win and relieve the pressure.
"We could have been more accurate but a win gives you a different mindset."
As well as Flood's 18 points, both Tuilagi and Dan Cole scored tries with Cockerill accepting the difference star players make.
He said: "When we've got our best players playing we are a good side. Quality players know how to play.
"You saw how Manu Tuilagi broke through tackling and offloaded quickly to create the last try."
Ben Youngs, the England scrum half was one player unable to return.
Cockerill revealed: "Ben's knee not great, he was unfit to play and there is no time span for his return. We have to monitor the injury."
Leicester travel to Sale in Aviva Premiership duty next, a match Cockerill acknowledges is "huge".
"A win was important tonight but next week at Sale is huge as league points are a priority."
Bryan Redpath, the Gloucester coach, accepted his side were second best while his pack were dominated in the set piece.
"They dominated proceedings. If you come here you have to get parity in the scrum and we have to accept we weren't good enough.
"Dan Cole and Marcos Ayerza are very strong. Under pressure there resulted in penalties and we were soon out of the mix."
Next week Gloucester resume Premiership action with a game against Saracens with Redpath still in positive mood for the fixture.
"We'll have Charlie Sharples, Mike Tindall, Eliota Sapolu and James Simpson-Daniel back in contention for next week. They'll provide us with a bit more zip."
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