Tigers were thankful for a 78th-minute penalty try in a 14-13 victory on a rain-lashed day in northern Italy and now have 14 points from four games, one ahead of Toulouse and five more than the Ospreys in a competitive pool.
“It was a tough afternoon but first of all you have to congratulate Treviso. They played the conditions very well, they played exceptionally well and they made us work exceptionally hard,” said Tigers director of rugby Cockerill.
“And you have to congratulate the lads in our changing room. They worked hard for it and got it in the end.
“We scored a good early try but we lost a bit of composure because of the penalty try against us.
“When things go against you it is easy to lose the game but the guys stuck at it, defended well when we had to and eventually got the result.
“I would never doubt the effort of the players. At the end I just wanted them to keep going because we were building pressure and I thought an opportunity would come and it would only take one of those opportunities to win on a day like this.
“Those bits of character can shape your season. You win when you could have lost and other sides drop points around you and that is massive for us.
“With the Ospreys winning against Toulouse we are in a good spot and the pool is wide open.”
Tigers travel to Swansea to face the Ospreys in Round 5 before a home match against four-time European champions Toulouse. Dates and times for both fixtures will be confirmed soon.
“In the end this is a good win for us but now we need to regroup and go back to the Aviva Premiership,” said Cockerill.
“Then we come back to the Heineken Cup and they will be a massive couple of rounds in the new year.”