The versatile defenceman-turned-left winger was equally surprised be named the NHL club's candidate for the Bill Masterton Trophy for perseverance and sportsmanship on Monday.
And he was chosen in a vote among local media for the Jacques Beauchamp Trophy as the player who made the best contribution to the team while not receiving any other honours.
"I think I'm the guy who is most surprised of all," the 29-year-old said. "At the beginning of the year if someone was to tell me I would be playing with Saku Koivu as a winger by the end of the year I'd say 'What? Impossible.'
"Even I'm surprised I can play forward in the NHL."
To which Koivu replied: "It works both ways. If someone had told me I'd be playing with Mark Streit, I'd have said: What?"
It was the lone light moment for Koivu on a day in which he was grilled by the media about being benched along with winger Michael Ryder for much of the third period as the Canadiens protected a lead in a 4-3 victory over the Buffalo Sabres on Saturday.
The night before, he was minus-4 and Ryder was minus-3 in a 5-2 loss in Ottawa. However, Koivu managed to score his 20th goal of the season - which ended up the game-winner - on one of his two shifts in the final frame against the Sabres.
He played only 12 shifts for about 11 minutes of ice time in the game, well below his 18:05 average. Ryder played one shift more.
"When you have 25 guys, it's impossible for everyone to be satisfied with the amount of ice time they get every game, that's just reality," said Koivu. "There are things a player can't control.
"Sometimes it's tough to imagine why it happened. You'd have to ask the coach. But as a competitor, I love playing in the last few minutes and you have to get a goal or defend a lead.
"But what's past is past. We won the game and now we have a huge game (Tuesday night). That's how I look at it."
The Canadiens, hanging onto the eighth and final playoff spot in the Eastern Conference, play the already eliminated Boston Bruins on Tuesday night at the Bell Centre.
They finish the season with games against teams also in the playoff hunt, Thursday night against the Rangers in New York and Saturday night in Toronto.
Coach Guy Carbonneau said Koivu's play in Ottawa was only part of his decision to cut his ice time.
"Also, the match-up I wanted with Saku's line wasn't there," he said. "It was the first time this year he's played less than 15 minutes, so it's not a big deal." The Canadiens have won eight of their last 10 games and Koivu has been a big part of the late-season surge, with two goals and 10 assists in that span.
The 32-year-old centre is just one goal and two points shy of his career highs of 21 goals and 71 points from 2002-03.
"When a team wins, you see success for individuals and that's been the case for me lately," he said. "But when there's so much on the line for the team in these next three games, you can't think about it too much.
"You hope you can get that goal and that two points and help the team at the same time."
While Koivu and Ryder sat, Streit continued to play.
The captain of the Swiss team that beat Canada 2-0 at the 2006 Winter Olympics has done a little of everything in his second NHL season. He plays defence and forward, kills penalties and works the point on the second power-play unit.
So far, he said he's only ever been in goal for street hockey while growing up in Bern.
The Canadiens drafted him 262nd overall in 2004. At his first NHL camp before the 2005-06 season, he looked totally lost, but gradually adapted. Last summer, he was given a new two-year contract at $US600,000 per season.
"After the Olympics last season he came back with a lot of confidence," Carbonneau said. "He never gave up."
Carbonneau called it "a great luxury" to have an extra defenceman playing forward who can move back to the blue-line if there is an injury.
At the start of the season, Streit was still on the fringe. He was a healthy scratch for the first four games of the season, and was scratched twice more after he returned to the lineup on defence.
But since he was moved to the wing in mid-season, he has been a regular, playing about 14 minutes per game. He has 10 goals and 25 assists in 73 games.
Now, even Streit is not sure if he should be called a defenceman or a forward.
"I don't know, I'm screwed up right now," he said with a laugh. "Whatever I'm asked to do, I'll do, but I think in my heart, I'm still a defenceman."
And now he'll have at least one unexpected team trophy to take home in the summer.
"Coming from Switzerland, nobody really believed I could make the team and be an NHL player, but I never lost my faith," he said. "I battled through and believed in myself and this year it paid off.
"I made the team and won a role on the team. I'm very happy. It's an unbelievable honour."
Streit is a longshot for the Masterton. It was last won by a Canadien in 2001, when Koivu took if after he battled back from abdominal cancer.