Tigers ran in five tries in a 38-13 victory at the Kassam Stadium in Oxford for a first opening-day win in the league since 2008.
Director of rugby Cockerill said: “I’m just happy to start with a win and the five points. For a first game of the season, away from home and against a new side, we can take a lot of the positives from the game and we can look at the negatives and where we need to improve.
“We did some really good things in the first half, we started to build a score and had control. But then we played poorly for a spell and they punished us. That got them a second wind in their sails and get back into the game.
“Welsh were very much up for the battle. We didn’t really know what to expect but there is enough experience in their side to cause you some problems.
“Everyone in the dressing room was calm at half-time and talked about being accurate and playing in the right areas and we thought the opportunities would come.
"We've got over the first hurdle and taken the points. Now we have to build for the next game, against Worcester on Saturday.”
Thomas Waldrom scored twice in the first half as Tigers led 17-10 at the break, with Julian Salvi, Geoff Parling and Premiership debutant Vereniki Goneva on the mark after the break.
“Goneva is still learning the competition but he is a good player,” added Cockerill, “And I thought Rob was very good today on his first appearance at this level. He did a lot of the hidden work you don’t see. It was good to get Jordan Crane and Boris Stankovich back out there too, and Brett Deacon got some time too. All-round it was a good outing for us.”
