Jereme Tendler gave the visitors the lead at the National Ice Centre when he fired home with 17 seconds of the first period remaining for his 30th goal of the season.
The Panthers were level, however, less than a minute into the second when Marc Levers found a way past Christian Boucher. Jade Galbraith was next to find the back of the net for the home side in the 33rd minute.
After Rob Bellamy stretched the Panthers' lead with a powerplay strike at 45.39, Stingrays were unable to find a response.
"It was a good game," said Cloutier afterwards. "Credit has to go to their goalie (Craig Kowalski) who made some big saves. Tendler had four breakaways but couldn't find a way past him.
"We had a good first period but in the second we were not ourselves and I was just disappointed that we didn't seem to want it more.
"The scoring chances were pretty even and we had some good chances but it wasn't to be."
The result saw Stingrays lose ground on rivals Coventry Blaze, whose 15-0 thrashing of the Edinburgh Capitals at the Skydome Arena saw them return to fifth in the table ahead of the Braehead Clan, who lost 4-0 at leaders Cardiff Devils.
Hull are now seven points behind the Blaze with two games in hand. They remain six points behind Braehead, but with five games in hand.
Cloutier's team are back in action on Sunday night when Cardiff Devils visit Hull Arena (6pm).
SATURDAY NIGHT SCORES
Cardiff Devils 4 Braehead Clan 0
Coventry Blaze 15 Edinburgh Capitals 0
Newcastle Vipers 2 Dundee Stars 3
Nottingham Panthers 3 Hull Stingrays 1
Sheffield Steelers 5 Belfast Giants 4