The Tigers earned a 25-18 victory over their Pool 3 opponents at Welford Road as they made a positive start to their European campaign.
While admitting that his side performed well against the Irish outfit, Cockerill is aware that there is a still a long way to go in the tournament.
"First half, we were pretty sharp, and second half we probably kicked the ball too much. I thought we could have scored another try in the first half, but we will take the win," he is quoted as saying by BBC Sport.
"We had to get off to a good start. I thought it was a cracking game, a good physical contest. It's one game, and it is good to win it. There is a long way to go, so we won't get too excited."
Leicester return to European action next Saturday when they travel to Wales to face Scarlets.