Tigers are two points behind the French heavyweights and Pool Two leaders, with only the group winners guaranteed a quarter-final place. Victory for Leicester would take them through, albeit to then face a potential last-eight clash away against European title contenders like Clermont Auvergne or Toulon.
"We have set the occasion up for next week. That was our aim, and it should be a classic," said Tigers rugby director Cockerill, following his team's 15-15 Liberty Stadium draw against the Ospreys.
"We are disappointed that we didn't win and won't have a chance to be at home in the quarters, but we are set up for a winner-takes-all with Toulouse at Welford Road.
"(Against) anyone at Welford Road we will back ourselves to beat them. Toulouse are a very good side. We know they have got the class in their team, and they know how to win games.
"But if we get past Toulouse, and that's an 'if' at this point, then we are in with a fighting chance."
Reflecting on the game, Ospreys head coach Steve Tandy said: "I am disappointed with the result - I thought we deserved more. It is a really deflated changing room.
"Most other teams would have thrown the towel in at 15-10 behind, but this group fights like no team I've seen or played in.
"They don't know when they are beaten, and they put in another massive shift."