Tries from Ben Youngs, Logovi’i Mulipola and Vereniki Goneva gave Tigers a third win in a row in the Aviva Premiership and moved them into fourth place in the table.
Director of rugby Cockerill said: “It was a bit frustrating that it was tight and nerve-jangling at the end, but it is a good win away from home.
“Irish have had two good away wins at Saracens and Wasps which set them up nicely for this game, but across the board I thought we were good. We deserved to win, it was by a small margin at the end but we created a lot of chances and scored three tries to nil.
“The forwards’ work was outstanding, we controlled field position really well and we were good value for the win.
“The performance can be better at times, but it is a good result and the boys can be pleased with their day’s work.
“We gave away too many penalties, our discipline was not as good as it should be, but it was a pleasing win.
“Now we’re in the top four with seven games to go. There is a lot of rugby still to come and we have to play a lot of the teams around us. We’ve been through a tough patch and we have to recover now and try to do the same at Newcastle next weekend.”
Owen Williams kicked a penalty and a conversion after starting at fly-half, and Cockerill was particularly pleased with his contribution alongside half-back partner Ben Youngs.
“I thought it was the right time to give Owen an opportunity and he did fantastically well,” Cockerill added. “He controlled it well, he kicked some important points in that wind and kicked field position well with Ben Youngs who looked sharp.
“Now we have to recover and try to do the same again at Newcastle next week. We won’t get ahead of ourselves and we’ve got a tough run-in but we will go out to play as hard as we can and see where it takes us.”
Anthony Allen and Matt Smith were late withdrawals from the Tgers squad at the Madejski Stadium, meaning a recall for Dan Bowden and a place among the replacements for Scott Hamilton.
“Anth just had a bit of a sore knee which wasn’t right and Matt had a tight hamstring after training yesterday which didn’t quite settle, but it was good to have Dan fresh and eager to play again, and Scott gave us that experienced option on the bench,” said Cockerill.