Tries from Matt Smith (2) and Marcos Ayerza , plus 16 points from scrum-half Julien Dupuy, ended a five-month wait for an away win in the Guinness Premiership and brought Tigers a first away win over Irish since the 2005/06 season.
“It is a great result for us,” said Cockerill.
“We were a bit disappointed that we let in those tries at the end which allowed one of our rivals to claim two points, but hats off to our lads.
“The attitude and the way we played, the attacking intent, was great. It takes some doing to win in that manner at Irish.
“The spirit and resilience of the players was second to none, I cannot speak highly enough of them.
“We deserved the game and it puts us right in the mix.”
Tigers have now scored 12 tries in the last three Guinness Premiership fixtures and Cockerill was happy that the attacking intent paid off.
“We scored three good tries and I think [backs coach] Matt O’Connor has got to take a huge amount of credit,” he said.
“His attitude with the players and in trying to use the backline is great and senior players have taken some ownership.”
Mike Catt, the London Irish coach who came off the bench as a second-half replacement to help steer their fightback from 28-11 in arrears, said: “It took us 20 or 30 minutes to get going. We could not get any go-forward. It was a great spectacle, a great game, but we need to win at home.”
Tigers return to home soil on Saturday for the visit of Guinness Premiership leaders Gloucester to Welford Road (kick-off 2.45pm). A limited number of tickets remain on sale from the Tigers ticket office. Call 08701 28 34 30.