Bath are the first visitors of the Guinness Premiership season to Welford Road this Saturday (kick-off 3pm) and the West Countrymen have been involved in some titanic tussles with Leicester over the years.
Cockerill, who played in many of those when the two clubs shared the top honours in the domestic game, said: "Bath had a big win last weekend against a good Worcester team, so we know they are playing well and they carry some threats."
The coach was understandably delighted by the 26-13 win at Bristol, but has warned his players that is now history and a new challenge stands in front of them.
"I told the players they had to go out and earn it at Bristol, and I think we earned the win," he said. "The commitment was second to none, we controlled the game exceptionally well and we took our chances.
"But what happened at Bristol is done. We are very happy that we won there, especially as we got nothing there last season, but Bath has to be our only focus. If we get ahead of ourselves or start thinking we are better than we actually are, we know Bath can punish us."
Tickets for the game remain on sale from the Tigers ticket office, call 08701 28 34 30, book online at www.leicestertigers.com or visit Welford Road.
Saturday will also feature the England versus Samoa match from the Rugby World Cup, shown in full 'as live' at Welford Road from 5pm. The scoreline in that match will not be announced at Welford Road!