The Warriors are currently four points adrift of closest relegation rivals Northampton with just eight games left - and their remaining league fixture schedule includes trips to title play-off contenders Gloucester, Sale Sharks and Bristol.
Worcester's Premiership home form this season - six defeats and a draw - has contributed immensely to their current predicament, although leaders Leicester have suffered four league losses on the road.
Despite Tigers standing 31 points and 11 places above their hosts, they will arrive at Sixways without rested England forwards George Chuter, Louis Deacon and Martin Corry.
Cockerill said: "Worcester are a good team, and in their last game they drew with Wasps - who are also a decent side. We will certainly not take them lightly.
"We have never found it easy at Sixways - and we have been upset there in previous years. We are not looking to invite an upset again."
Worcester's situation will deteriorate if Leicester take the points and Northampton, boosted by the return of fit-again captain Bruce Reihana, can overcome Franklin's Gardens visitors Harlequins on Saturday.
Quins claimed their first scalp of the Premiership campaign when they beat Saints in early November, and Northampton have won just two subsequent league games - defeating Worcester and Wasps. But the Reihana factor could inspire them against a Quins side struggling for consistency.
The New Zealander has not made a senior start since suffering serious knee damage at Gloucester in September - and he said: "To be able to lead the boys out of the tunnel again will be very exciting.
"But I have just got to keep my emotion inside a bit and channel my energy into my role on the pitch."
Quins are bolstered by back-row forward Nick Easter's return from England duty.