Cockerill has led his men to back-to-back Premiership titles, with the Tigers having reached six successive English finals, but he is yet to taste success in Europe as head coach or director of rugby.
The former England hooker conjured up a finals appearance within his first six weeks in sole charge back in 2008/09 but the Tigers failed to qualify for the knockout stages for only the fourth time in 13 seasons.
And with years of experience as a player and a coach at Welford Road, Cockerill knows just how vital it is to at least reach the last eight this time around.
"Getting out of the European group is massively important for the club, both playing wise and financially," said Cockerill.
"You want to be at the top table in Europe. We've done it well historically.
"Last year was disappointing, but if you look at our group, the English team were champions of their country, the French team were the reigning champions of their country, the Welsh side were champions of the Celtic League later that season, and the Italian team were runners up in their league. It was a very form orientated group for that season.
"Every year, the competition gets more difficult. There's a lot of good sides and a lot can happen. You've just got to put yourself in a position to qualify and then one-off games are exactly what they say they are."
Leicester started life in this year's Heineken Cup with an almighty scare, trailing at Treviso until a late Alesana Tuilagi try saved them from a first defeat to Italian opposition.
In contrast, the Scarlets crushed French giants Perpignan in Llanelli with an outstanding display that brought back memories of their unbeaten march to the Heineken Cup semi-finals in the 2007/08 campaign.
Ironically, it was Leicester who were on top form to end the Scarlets' challenge three-and-a-half years ago, and Cockerill knows a similarly commanding performance will be required to take the spoils on Sunday.
"They scored some cracking tries and one of them was as good as you will see," added Cockerill.
"Stephen Jones and Regan King are quality players.
"They are great with the ball in hand but, like us, have been conceding too many tries. You never know. It might be a 65-64 thriller.
"I know Robin McBryde (Scarlets forwards coach) very well. I played against him and he's obviously done a very good job with the Welsh side.
"They've got some good players; they're well coached; they've got great facilities and they've got all the ingredients to be good side."