But Tigers had to fight for the five points in round one as Alesana Tuilagi scored a last-minute converted try to secure a 34-29 win at the Stadio Monigo.
Tigers director of rugby Cockerill said: “It’s a good result, we scored five tries and got the bonus point against a good Treviso side.
“We were a bit inaccurate at times, but we created opportunities, we scored five tries and we have five points.
“Nobody has scored a bonus-point try here this season so we have got to be upbeat going into next week’s home against against Scarlets.
“Many other sides might have given up today, but we kept going and we got the result."
Tigers lost Toby Flood and Ben Woods in the build-up to the game and then saw Dan Hipkiss withdraw during the warm-up, but still managed scores from Matt Smith, Craig Newby, Martin Castrogiovanni and Ben Youngs before Tuilagi’s decisive contribution.
“The changes don’t help with continuity or the defensive organisation, but we just had to get on with it,” said Cockerill.
“We were never going to take Treviso lightly because we know they are a good side. Now we go on and we have a home game against the Scarlets. They started with a good win and we know this is going to be a very competitive pool.”
Tigers return to home ground this Sunday when they host Scarlets, who beat Perpignan in their opening match. Tickets are on sale now.
Secure your slice of European rugby action by contacting the Tigers ticket office now. Book online by clicking here, phone the hotline on 0844 856 1880 or call in at Welford Road (8.30am-5pm weekdays, until 8pm on Wednesday and from 9am on Saturday.