The Jets' playoff chances disappeared before their 4-2 loss to the Montreal Canadiens on Thursday.
Winnipeg finished ninth in the Eastern Conference, one spot out of the playoffs and better than last season.
"I'm going to have a hard time drawing on any positives you know, when you're going home and watching the important hockey being played from your couch again," Wheeler said.
"Hopefully we can all look in the mirror and make a change, I think we're on the right path, but ninth place is a first-class ticket home."
The Jets were ahead 2-1 as they started the third period, but most already knew their result wouldn't be enough to advance.
"We knew after the second we are out," goaltender Ondrej Pavelec said.
"It's not an excuse at all but it's tough to play when you know you've got 20 minutes left in the season."
Both the New York Rangers and Ottawa Senators clinched playoff spots with overtime wins Thursday night.
David Desharnais scored the go-ahead goal for Montreal, which came on strong in the third. Rene Bourque, Max Pacioretty and Brendan Gallagher had the others as the Canadiens (28-14-5) broke out of a slump that had seen them lose five of their previous six games.
James Wright and Wheeler scored for the Jets, who finished the season 24-21-3.
Montreal's win keeps it in the hunt for the top spot in the Northeast Division where it remain tied with Boston.
But the win guarantees the Canadiens at least fourth in the East and home-ice advantage in the first round of the playoffs.
"It's a big win against a desperate team," Montreal captain Brian Gionta said.
"It's huge. Home ice is really big in the playoffs. ... You keep forcing plays, you keep being relentless on the puck, eventually they're going to turn it over and they're going to get tired and we took advantage in the third."
Canadiens defenseman P.K. Subban, who had two assists Thursday night, agreed with his captain.
"You want to use that fan base to your advantage. Now that we've got home-ice advantage we want to use that."
The game started well for the Jets.
Chris Thorburn and Wright teamed up in the first to put the Jets ahead 1-0. Wright's wrist shot from the slot found the upper corner of the Montreal net.
But the Canadiens still managed to spend a lot of time in Winnipeg's zone.
The Jets were outshot 8-5 in the first and had managed only two more midway through the second when Bourque evened things up.
His shot from the faceoff circle found its way through a mad scramble in front of the Winnipeg net.
Wheeler put the Jets ahead again about five minutes later when he dug a puck out of a scrambling Carey Price in front of the Montreal net and slipped it in.
The third was only about two minutes old when Pavelec intercepted Gallagher's shot, only to see it rise high in the air and bounce behind him, dribbling over the line before he could grab it.
Desharnais then scored on a 5-on-3 in the third to put the Canadians ahead for the first time.
Pacioretty scored later in the period for a little insurance.
The Jets looked like a good bet to make the postseason until a five-game slide. Even a 6-1-1 record in their last eight games failed to make up all the lost ground.
Their only chance was to win Thursday and have both New York and Ottawa lose all their remaining games.
Coach Claude Noel said he would talk about Winnipeg's season and future Friday and confined his brief comments to the game.
"I thought the game was OK. They spent too much time in our zone, which I didn't really like. ... I would have liked us to play with a little more zip in the first two periods," he said.
- Jets captain and scoring leader Andrew Ladd finished the season with the best points-per-game average by a Jets (Thrashers) player since Ilya Kovalchuk in 2008-09.