Tigers are top of Pool 3 but must travel to Swansea to face the Ospreys, the only team that can overhaul them, in the final round of fixtures next Saturday.
“We’re very happy with the win,” said forwards coach Cockerill. “It was a bit scrappy at times but we got a good start and scored the tries we needed.
“We have put ourselves in a position now where we can still qualify and that is what we wanted at this stage.
“The attitude of the players all week was great and we went into the game wanting to play quickly. We had to score tries, it was as simple as that.
“Treviso can be stubborn opponents so we are pleased with the outcome.
“It was 40-0 at half-time and we were a bit more accurate than we have been in the last few weeks. We will take the points and move on to next week and another massive game for us.”
Munster, Harlequins and Cardiff Blues have already confirmed their places in the Heineken Cup quarter-finals and they will be joined by the remaining three Pool winners and the best two runners-up.
“It is going to be very difficult there, Ospreys are a dangerous side,” said Cockerill.
“They will come at us very hard. It is going to be an interesting game - but this is what the Heineken Cup is all about.”
