Edinburgh host Cardiff at BT Murrayfield on Saturday evening in the quarter-finals hoping to reach the final four for the first time since 2015, when they went on to finish runners-up in the second-tier competition.
It has been some start to life north of the border for Cockerill, who inherited a struggling side but has so far led them to the quarter-finals and third place in Conference B of the Guinness PRO14.
They are currently on a hot streak of five successive wins in the league and could seal a play-off place against Ulster next week, but Cockerill is refusing to prioritise one competition over another and has warned his players that they will have to be at their best if they want to advance.
“Our season is alive and if we lose on Saturday we are out,” the Edinburgh head coach said. “I don’t think we are a good enough side or experienced enough at this point to get too far ahead of ourselves. We need to keep working hard and it’s worked very well for us so far.
“This season is not over and not a success just yet because we still have lots to play for.
“At some point the bubble will burst and some point we will hit the road bump that derails us a little bit and we have to make sure we get back on task.
“At this point, we are in Europe and want to go as far as we can, and we are in a good position in the league and want to go as far as we can.”
Cockerill has named a strong side to face the Blues on Saturday, with hooker Stuart McInally returning from Scotland duty and Darryl Marfo dropping out of the 23 after making his comeback from injury against Connacht last week.
Hamish Watson is absent due to a shoulder problem while Sam Hidalgo-Clyne is still suffering from a head injury. Captain Fraser McKenzie will make his 100th appearance when he features in the second row alongside Grant Gilchrist.
The sides have not met since Cockerill’s first game in charge, when Edinburgh emerged 20-10 winners, but he is expecting a different game this time around.
He said: “We are both different teams. I think we’re a better side and I think they’re a better side.
“At the start of the season they were in a little bit of turmoil, but they have sorted their coaching out and Danny Wilson is a good coach and doing a good job.
“We can’t be at 90 per cent because we’re not good enough to cruise through games. We have to be at our best to win.”
Edinburgh: 15. Blair Kinghorn 14. Dougie Fife 13. Mark Bennett 12. Chris Dean 11. Duhan van der Merwe 10. Jaco van der Walt 9. Nathan Fowles 1. Jordan Lay 2. Stuart McInally 3. WP Nel 4. Fraser McKenzie (capt) 5. Grant Gilchrist 6. Magnus Bradbury 7. John Hardie 8. Viliame Mata. Replacements. 16. Neil Cochrane 17. Rory Sutherland 18. Simon Berghan 19. Lewis Carmichael 20. Cornell du Preez 21. Sean Kennedy 22. Duncan Weir 23. Phil Burleigh.
Cardiff Blues: Gareth Anscombe; Blaine Scully, Rey Lee-Lo, Willis Halaholo, Owen Lane; Jarrod Evans, Tomos Williams; Gethin Jenkins (capt), Kristian Dacey, Dillon Lewis, George Earle, Josh Turnbull, Josh Navidi, Ellis Jenkins, Nick Williams. Replacements: Kirby Myhill, Rhys Gill, Anton Peikrishvili, Seb Davies, Macauley Cook, Lloyd Williams, Garyn Smith, Matthew Morgan