Tigers earned a 32-18 victory away to the Scarlets last weekend to stay in the hunt for a quarter-final place from Pool 5 with just one fixture remaining.
“Sunday’s game is as important as last week’s and there is no thought of taking our foot off the gas,” said director of rugby Cockerill.
“We have got to get it right mentally, get the preparation right and go for it.
“The win last week has put us in a position to be able to qualify, but we have not done anything yet.
"We need to win again. Treviso have a lot of experienced international players, they did very well against us earlier in the season and we will not be taking them lightly.
“We have got ourselves into this position by winning a very important game away from home against a very good Scarlets side last week. We needed to win to keep any chance of qualifying and we won it under pressure so that bodes well for us.”
Tigers welcomed back Scott Hamilton for the win at the Parc y Scarlets after his return from New Zealand, but captain Geordan Murphy is sidelined with an ankle injury.
“Geordan will have surgery on his injury in the next week or so and until then we won’t know how long he will be out,” said Cockerill.
“He is massive for us as a leader and as a player but we have to get on with it and someone else has to step up.”
Tickets for Sunday’s must-win match are still available from the Tigers ticket office.
Phone the hotline on 0844 856 1880 or call in at Welford Road now. The ticket office is open until 8pm on Wednesday, 8.30am-5pm Thursday-Friday, 9am-5pm Saturday and from 9am on Sunday.
Or book online by clicking here.
