The Tigers came unstuck 30-12 in France last time out - although their challenge wasn't helped by having Manu Tuilagi and George Chuter sin-binned.
The defeat saw the former Heineken Cup champions drop to third - and Cockerill knows his side need to bounce back.
"Last week's match was a tough, full-blooded encounter," he said. "It was as intense as any international match and we cannot fall off from that level this week.
"Clermont have an extremely strong squad with quality across the board but the scoreline was not very flattering for us last week and we know we have to be much better in terms of accuracy and when you get your chances you have to take them against a top-quality side."
Cockerill has recalled Thomas Waldrom to his starting XV while Boris Stankovich and Ben Woods have been named on the bench.
Pool leaders Clermont have made seven changes to their line-up.
David Skrela and Regan King have been added to the back division, while Jason White, Jamie Cudmore, Ti'i Paulo, Lionel Faure and Clement Ric form a new-look front-five.
Leicester Tigers: 15 Geordan Murphy, 14 Horacio Agulla, 13 Matt Smith, 12 Manu Tuilagi, 11 Alesana Tuilagi, 10 Toby Flood, 9 Ben Youngs, 8 Thomas Waldrom, 7 Jules Salvi, 6 Tom Croft, 5 George Skivington, 4 Louis Deacon, 3 Martin Castrogiovanni, 2 George Chuter, 1 Boris StankovichReplacements: 16 Rob Hawkins, 17 Julian White, 18 Dan Cole, 19 Steve Mafi, 20 Ben Woods, 21 Sam Harrison, 22 Billy Twelvetrees, 23 Scott Hamilton.
ASM Clermont Auvergne: 15 Lee Byrne, 14 Sitiveni Sivivatu, 13 Regan King, 12 Wesley Fofana, 11 Julien Malzieu, David Skrela, 9 Morgan Parra, 8 Julien Bonnaire (c), 7 Alexandre Lapandry, 6 Gerhard Vosloo, 5 Jason White, 4 Jamie Cudmore, 3 Clément Ric, 2 Ti'i Paulo, 1 Lionel Faure. Replacements:16 Benjamin Kayser, 17 Vincent Debaty, 18 Daniel Kotze, 19 Nathan Hines, 20 Elvis Vermeulen, 21 Kevin Senio, 22 Brock James, 23 Gavin Williams.
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