"We wanted to play today and we took our opportunities to score those first three tries very well and then we had three or four more opportunities to score that we didn't take," Cockerill told reporters.
"There were probably five or six tries left out there from both sides. We need to be more accurate.
"We needed the five points and that was good for us. It keeps the pressure on Ulster but they're in the box seat. We've got to win next week at Montpellier really."
Leicester trail Ulster by two points in the group.