Stingrays will finish the regular season table in bottom place should they fail to overhaul Newcastle Vipers, who enter the final weekend three points ahead with two games to play.
Hull must hope that they can win their two home games against Cardiff Devils (tonight 5.30) and Sheffield Steelers (tomorrow 6.00), while Newcastle slip-up in their matches against Belfast Giants and Nottingham Panthers.
While Cloutier admits he would prefer to avoid the wooden spoon, he is more than happy with the improvement shown by his side in the last three months, with 22 points coming from the last 20 games.
"It is frustrating when you see what we have achieved with a fully-fit squad," said Cloutier.
"It was pretty bad in the early part of the season. We only had 10 or 11 players which made it hard to even practise let alone fully compete in matches and we had no confidence.
"But the guys have worked their socks off and it would mean the world to everyone at the club to make it to Nottingham for the play-off finals weekend.
"We are playing some good hockey and the self-belief is now there."
While Hull battle it out at the bottom with Newcastle, Steelers will hope to clinch fifth place ahead of Edinburgh Capitals, thereby securing a two-legged play-off against Cardiff Devils.
Despite only picking up one point from last weekend – from an overtime defeat at home to Hull – Dave Matsos's side have improved in recent weeks.
Having already meekly surrendered their league title, they will hope to salvage their season by sealing a third straight play-off triumph.