The 1998 Nagano Olympics was the first time the NHL sent its players, and it was the first time Price can remember watching them.
Expectations were high for Canada to end a 46-year Olympic gold medal drought in men's ice hockey, as no longer was the national team armed with the excuse of being deprived of the country's best players. Price was no different than his fellow Canadians.
Except not only did Canada fail to win gold, the team failed to reach the podium after losing the bronze-medal game to Finland, making it a milestone in Price's memory.
"That was the first time I remember watching Team Canada and being disappointed," Price told NHL.com. "So that was my first real memory of the Olympic Games."
In February there will be a legion of similar 10-year-old boys across Canada watching the men's hockey tournament at the 2014 Sochi Olympics, and Price would love nothing more than to have the opportunity to make their memories positive ones.
It's something Price has wanted from the moment he entered Hockey Canada's Program of Excellence at the 2004 World Under-17 Hockey Challenge, where he won a silver medal with Team Pacific. He went on to win a silver medal at the 2005 IIHF World Under-18 Championship and gold at the 2007 IIHF World Junior Championship.
"I think once you start playing in the Hockey Canada program," Price said, "that's when [going to the Olympics] becomes a long-term goal."
But in order to reach that goal Price will need to come out on top of what is a wide-open race to claim one of the three goaltending spots for Canada, and he knows his play with the Canadiens over the opening months of the NHL season will be the only way he will give himself a chance to make that happen.
However, Price insists that the looming Olympics had no impact on his offseason preparation, and the way the 2012-13 season finished likely had a role to play in that.
The Canadiens struggled to prevent goals down the stretch after competing all season for the top spot in the Eastern Conference, allowing 31 goals over the final eight games of the regular season to finish on a 3-5-0 slide. It extended into the Stanley Cup Playoffs, where Montreal allowed 20 goals in a five-game first-round loss to the Ottawa Senators.
Price allowed 37 of those 51 goals in 11 starts, and his season ended when he hurt his knee while the Senators scored with 22.6 seconds remaining in regulation to send Game 4 into overtime, eventually winning it by scoring on backup Peter Budaj at 2:32 of the first overtime.
In just under three minutes of game time the series went from being tied 2-2 to the Senators being ahead 3-1, and they closed it out in Game 5 with a 6-1 win while Price watched in street clothes.
Price has been reluctant to speak about how last season ended, but it's pretty clear he had no need for any added Olympic motivation over the summer to come back strong and perform well this season. Still, the idea that Canada executive director Steve Yzerman is watching remains present in Price's mind.
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"I thought about it a few times over the summer, but it doesn't really change my preparation a whole lot. I wanted to play well here," Price said. "But it's definitely in the back of your mind. You want to play well and you want to be recognized by [Yzerman] in order to make that team. But the only way to do that is to play well here."
Knowing he has a few extra sets of eyes from Hockey Canada's braintrust watching his every move is one thing that will not bother Price, not when he's played in the Montreal fishbowl his entire career.
"There's always eyes on us here, so I don't really feel any added peepers on me," Price said with a laugh. "I still have to perform well. Regardless of the opportunities presented, my goals are still the same with this club as they would be if there wasn't the Olympics.
"It definitely would be fun to take part in that. Obviously I'd like to start and win a gold medal for our country. But for me it's one step at a time. In order to get to that position I need to play well at this position."
The end to Price's season, however, did not significantly damage his chances of going to Sochi in February. In fact, that degree of doubt almost made him a typical candidate for the Canadian net.
The goaltending position has been pegged as Canada's biggest question mark heading into the Olympic tournament by most pundits, experts, fans and just about anyone with an opinion on hockey. It was something that was made clear to Price and the four other goaltenders who attended Hockey Canada's Olympic Orientation Camp in Calgary in August by the constant questions from the media on this very subject.
If it wasn't Price's poor finish last season, it was Roberto Luongo losing the starting job with the Vancouver Canucks to American goalie Cory Schneider, or Mike Smith's difficult season with the Phoenix Coyotes, or Corey Crawford's relative lack of pedigree despite backstopping the Chicago Blackhawks to the Stanley Cup, or the inexperience of Washington Capitals goaltender Braden Holtby.
That's leaving out the goalies who weren't invited to the orientation camp but who remain strong candidates to make the team, like Marc-Andre Fleury of the Pittsburgh Penguins, Cam Ward of the Carolina Hurricanes or even dark-horse candidates Devan Dubnyk of the Edmonton Oilers and Jonathan Bernier of the Toronto Maple Leafs. And then there's one of the greatest goaltenders in NHL history, 41-year-old Martin Brodeur of the New Jersey Devils.
Not a single one of those goaltenders can be seen as a slam-dunk pick for any of the three spots on the Canadian team at this point, and that reality has a nation of hockey fans nervous.
But not Price.
"It's kind of disappointing," he said of the cloud of doubt hanging over the goalie situation. "I feel like we have a lot of really good goaltenders in this country. I think that's been a strong point in our program for a long time. I think the biggest reason is that we don't have those standout guys that have been there for two or three Olympics, so I think everybody's viewing it from a different point of view.
"But we have the defending gold medalist [Luongo], we had a Stanley Cup champion from last year at that camp, I've won a gold medal for this country before. I really don't see where this perspective is coming from."
It would not fit Price's laid-back demeanor for him to get angry over the lack of confidence shown by Canadians in him and his goaltending brethren. The ability to ignore criticism and remain focused is something he has had more practice at than he probably would have liked during his time in Montreal, now already in its seventh season despite Price's young age of 26.
But that doesn't mean the chorus of doubt hasn't had an impact on him.
"Does it make me angry? No," Price said. "I think motivated would be the best word."