Richard Cockerill admitted his frustration after Leicester failed to secure the bonus-point against Aironi in northern Italy.
The Tigers dominated the first half 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.
Cockerill was disappointed with his side's lack of killer instinct, saying: "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 added: "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."
Cockerill was also critical of the way Scottish referee Neil Paterson officiated the encounter
"It was very difficult to play in the second half," he said.
"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. (Leicester captain) Geordan (Murphy) 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."