The Tigers dominated the first half of the Heineken Cup contest and led 20-6 at the interval following tries from Tom Croft and Alesana Tuilagi.
But they made hard work of it following the restart as the Italian outfit demonstrated far more steel and it was not until the 80th minute that the Tigers scored their third and final try through Niall Morris to secure a 28-12 victory.
Cockerill was disappointed with his side's lack of killer instinct but was also critical of the way Scottish referee Neil Paterson officiated the encounter.
Cockerill said: "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.
"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. They defended very well and the breakdown wasn't particularly well refereed. They just tackled and lay at the back of the breakdown, we couldn't get any ball to play.
"If you cheat enough you only really get pinged for the really serious ones. We just couldn't get any ball which is disappointing.
"We were 7-1 up on the penalty count after 20 minutes because the referee refereed the breakdown and they had a guy sent to the bin but as the game wore on the offences were getting penalised less.
"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, who won back-to-back titles in 2001-2002, welcome Ulster to Welford Road in next weekend's European action.
Cockerill has called on his side to build on the result and also hopes to welcome injury victims Ben Youngs and Billy Twelvetrees back to action.
He added: "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.
"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."
Meanwhile Aironi face a daunting trip to Clermont-Auvergne with several injury concerns over Simone Favaro, Nicola Cattina and Fabio Ongaro.
Aironi head coach Roland Phillips insists his side must approach the game in the same manner and continue to build.
He added: "Mentally we approach the game in the same way. They have a star-studded team just like Leicester. But we need to focus on ourselves and continue to improve.
"We are building something, we have to believe and stick to our processes."
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