And that disappointed Cockerill, but the former England hooker was determined to take the positives from the game.
"It's an away win which is difficult to get in Europe but we had enough opportunities to score more tries, certainly in the first half," he said.
"This tournament is very difficult and there's a long way to go. You have to take the win and take the positives.
"But we probably should have taken more advantage of that first half-hour.
"It was very difficult to play in the second half and they defended very well.
"But we had opportunities to score more. Geordan dropped the ball early in the game and there were chances all over the place. "
"We were a bit loose at times with ball control and that cost us."
The Tigers return to Welford Road next weekend to host Ulster and Cockerill is hoping to call upon the returning Ben Youngs and Billy Twelvetrees.
"We need to win next week at Welford Road - you have to keep winning in this competition. But they are a good side with some very good individual players," he added.
"It is a massive game for us. These are the deciding games of the season and if we come away two from two and with eight or nine points then that will be a huge plus.
"We hope to have Billy and Ben available for selection but how much they will be involved remains to be seen."
"But the positive is, from today there are no further injuries."