The champions host the current Guinness Premiership leaders at Welford Road on Saturday in a rematch of last year's play-off final.
Both sides have won their opening three matches of the season but Gloucester have secured two more bonus points than the Tigers.
"The players are to be congratulated on their efforts so far, but the challenges do not get any easier and we need to keep improving," said Tigers acting head coach Cockerill.
"Those three wins will mean nothing when we run out against Gloucester. They have started the season extremely well and, on form, they will be favourites, which is unusual for us at Welford Road.
"This is a difficult part of the season for us and we need that famous Welford Road support right behind us, just like it was in the game against Bath two weeks ago."
Cockerill remains in charge of team affairs with new coach Marcelo Loffreda not due to arrive until after Argentina's involvement in the World Cup ends.
Both sides are still without a whole host of World Cup players but Gloucester fly-half Ryan Lamb does not believe there will be any drop in intensity.
"Leicester away is always going to be a tough test," Lamb told the Gloucester Citizen.
"They've started really well with a depleted squad, like we have, and so it's going to be good. We're all looking forward to it."
Lamb's position in the side, particularly as goalkicker, could be under threat soon with Scotland playmaker Chris Paterson due to arrive at Kingsholm after the World Cup.
But the 21-year-old is just concentrating on his own game and not worrying about the form of Paterson, or even that of Jonny Wilkinson, who blocks his route to the England team.
"Ten is a big position and people like Jonny and Chris know how to play it," he said.
"I'm not going to jump in and say I can do something that I'm not prepared to put in on the pitch. I'm just trying to kick my goals as often as I can."