The former England hooker, looking ahead to his first game in charge as Leicester Tigers acting head coach, said: "I want us to turn up and put in a good performance. Our boys have a responsibility to make sure we get off to a good start."
Even without 11 senior players on international duty, as well as Aaron Mauger and head coach Marcelo Loffreda who arrive after the Rugby World Cup, Cockerill is in a positive frame of mind and is backing his current squad.
"When the World Cup guys return, I would like us to be in the top four or five in the Premiership. You have to have those ambitions, but we are not waiting for the guys to come back before our season starts. That is no disrespect to those players, it is just a fact we have to get on with.
"Even with those guys away, there were some tough selection calls, especially in the pack and in the back five of the pack in particular.
"It is about getting the balance right for this weekend and also countering what Bristol will throw at us. Bristol are a good team, they beat us well down there last season, they finished not far behind us and they are in the European Cup. We are under no illusions about the task ahead of us.
"We have got to stop making unforced errors and do the simple things well. I am sure every coach will be saying that. I said last week we were ready for a meaningful game and we have certainly got that down at Bristol."
Cockerill's first league selection includes new signings Benjamin Kayser, Boris Stankovich, Marco Wentzel, Owen Finegan and Ayoola Erinle.
