"You always want to win that gold medal," Pietrangelo said. "What we did tonight, and what we did New Year's Eve, was remarkable.
"The guys we have in that room are friendships I'll keep for a lifetime.
"They were unbelievable character guys to go through this with. It's unfortunate, but we have to hold our heads high."
Jordan Eberle singlehandedly brought the Canadians back from the brink of defeat late in the third period.
Eberle scored twice in 1:14 -- the second with just 1:35 remaining in regulation -- to force extra time.
American captain Derek Stepan, who gave his team a 5-3 lead in the third period, said Eberle's heroics were nothing new to him.
"We all knew about him before," Stepan said. "He's a real special player.
"For him to have games like that consistently, it's something special.
"That kid is going to play in the NHL for a very long time."
The U.S. thought they had it won when they scored twice in 2:11 in the third period to seize control.
Jerry D Amigo scored on an odd-man rush before the heartbreaker came moments later.
Canadian goaltender Jake Allen inexplicably kicked a dump-in back into the slot and Stepan made no mistake.
Allen, who looked shaky throughout, was replaced by Martin Jones.
Canada had a chance to win it in overtime, but after U.S. goaltender Jack Campbell made a big stop, the Americans turned up ice on an odd-man rush.
Carlson unloaded a slapper from the hashmarks to win it.
Luke Adam, Greg Nemisz and Taylor Hall have lit the lamp for Canada with Chris Kreider and Jordan Schroeder also scoring for the Stars and Stripes.
The Americans got the go-ahead goal on the powerplay 1:03 into the middle frame as Carlson's point blast beat a screened Allen to the stick side.
Hall got Canada back on even footing on a strange shot from the outside that bounced over American starter Mike Lee.
That spelled the end of the night for Lee, who was beaten three times on seven shots.
Jack Campbell took over between the pipes and turned aside all 12 shots he faced.
The shots were 25-19 for the U.S. after two periods.
The sold-out crowd at the Credit Union Centre worked itself into a frenzy and greeted Team Canada with a thunderous roar as the players took to the ice.
And they didn't have to wait long to explode once the game began as Adam took a pass from Jordan Caron in the slot and slid a backhander five-hole on American starter Mike Lee.
Team USA forward Tyler Johnson, who scored a shorthanded goal against Canada New Year's Eve, turned on the afterburners and got a partial breakaway.
But he was hassled from behind and crashed hard into the end boards near the midway point of the period.
Gabriel Bourque nearly expanded Canada's lead shortly after but his backhander deflected just over the net.
It took the Americans just 36 seconds to wipe out the defecit and build a lead of their own.
Kreider sent a wrister over Allen's glove after Canada turned the puck over in the neutral zone and then Schroeder also beat Allen's glove to put the U.S. up 2-1.
But the Canadian killed that momentum when Nemisz, the only Canadian skater without a point in the tournament to that point, picked up an errant pass in the slot and beat Lee to the short side.
Goal: Benjamin Conz, Switzerland
Defence: Alex Pietrangelo, Canada; John Carlson, USA.
Forwards: Jordan Eberle, Canada; Derek Stepan, USA; Nino Niederreiter, Switzerland.
Best goaltender: Benjamin Conz, Switzerland
Best defenceman: Alex Pietrangelo, Canada
Best forward: Jordan Eberle, Canada