In a rare move, Pedersen penalised Canada goalkeeper Erin McLeod for holding the ball for too long after making a save in the 80th minute, awarding the U.S. an indirect free kick in the penalty area.
The law states the goalkeeper should release the ball after six seconds, but it is hardly ever applied in either men's or women's football.
While that decision appeared to Canada's team to be harsh, Pedersen then awarded the U.S. a penalty resulting from Megan Rapinoe's free kick. The ball struck the elbow of Canadian Marie-Eve Nault with the player turning away.
The referee was not available for comment.
A spokesman for FIFA said: "As is our practice, FIFA will make no comment on this issue and in any case, the referee's decision is always final."
Canada's coach John Herdman initially shied away from the controversy but then added: "She's got to live with that. We will move on from this. I wonder if she will be able to."
McLeod told reporters: "The referee said I had the ball for 10 seconds. She obviously counted the time I was on the ground with the ball. Once I got to my feet I calculate I only had the ball for five seconds.
"We feel like we got robbed in this game. The referee was very one-sided. I have never known this to happen before in a game, referees never make this kind of decision."
Skipper Christine Sinclair, who scored all three of Canada's goals, added: "When she gave the penalty, she giggled and said nothing, Classy!
"In an important match it's a disappointment the referee had such an impact on it. We feel cheated."
Canada will meet France for the bronze medal on Thursday but Sinclair added: "Maybe the referee will wear a Canadian jersey for this game."
Canada had already felt hard done by at these Games when equestrian rider Tiffany Foster was disqualified before the team show jumping final on Sunday because of hypersensitivity in her horse's front leg, a decision team captain Eric Lamaze called "a complete miscarriage of justice".
The match was as dramatic as the scoreline suggests with the winning header from U.S. striker Alex Morgan coming three minutes into added time at the end of extra time.
Canada led three times thanks to Sinclair's goals with the U.S. equalising each time, twice through Rapinoe and once from Abby Wambach's contentious penalty which took the game into extra time.
Thursday's gold medal match is against Japan at Wembley where the U.S. will aim to win their third successive Olympic title against the team that beat them on penalties in last year's World Cup final.