After Saturday's win, Cockerill admitted: "We know exactly what we need to do."
His men rescued their European campaign from the perils of possible group stage elimination by staging a superb second-half fightback against French heavyweights Clermont Auvergne to win 23-19 at Welford Road.
It means that Leicester, Clermont and Ulster - comfortable 46-20 winners over Italian strugglers Aironi on Saturday - remain in the Pool Four shake-up with only one quarter-final place guaranteed.
Leicester go to Belfast when the tournament resumes next month, then end their campaign at home against Aironi. They are currently two points behind Ulster and one above Clermont.
"To quality from these pools you need to win five of your six games," former England hooker Cockerill said.
"So we know exactly what we need to do, which is beat Ulster in Belfast and Aironi at home."
The Tigers, European champions in 2001 and 2002, appeared to have little chance of progressing from the group when Clermont cruised into a nine-point interval lead.
But Leicester rapidly wiped out that deficit before Toby Flood's 62nd and 72nd-minute penalties secured the points and kept Tigers on course for an 11th quarter-final appearance in 15 seasons of Heineken Cup rugby.
Cockerill added: "We were composed at half-time, and I didn't think we were overly poor in the first half, but we did give away too many turnovers and we also conceded a cheap try.
"That meant we were up against it because Clermont are a very good side, but we regrouped and turned things around.
"Reaching the quarter-finals is the priority. Who you might meet, and where, comes later."
England centre Manu Tuilagi and flanker Julian Salvi scored tries for the home side, while Flood kicked 13 points.
Clermont's ex-New Zealand wing Sitiveni Sivivatu touched down for the visitors, while Morgan Parra and David Skrela both dropped goals, with Parra also slotting two penalties and a conversion.
But it was not enough during a game when the lead changed hands five times as Leicester narrowly staved off suffering a first European home defeat in five years since Munster beat them 21-19.
Clermont's losing bonus point, though, could yet prove important to the final pool picture, which is a prospect not lost on their captain Julien Bonnaire.
"We kicked the ball out at the end because it made sure that we will go home with a point," he said.
"We were very positive before the game. We came here to win and we believed we could win against Leicester twice in a row (Clermont triumphed 30-12 in France last weekend).
"When you look back after a qualifying group and you have taken a point in Leicester, then it could be the point that takes you into the next stage of the competition."
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