Hayes, who took over in late May after leaving her role with club team Chelsea, guided them to victory in Saturday's Olympic final with a 1-0 win over Brazil.
It is a fifth gold for the USA but one that many had doubted they were capable of winning after their early exit from last year's women's World Cup.
Being knocked out in the round-of-16 was the worst performance by a USA team in a World Cup but Hayes has rejuvenated the team.
"Joy and belief have been the two biggest words for us. We have had so much fun," said forward Trinity Rodman when asked about Hayes' impact.
"But we have still pushed each other really hard. I think there is a misconception that 'Oh they laugh and dance all the time in training, they're not serious' but we just proved to everyone that we are and we take this very seriously," she said.
"Emma has brought a lot to the group, a lot of energy, a lot of connection. But at the same time we have learnt from a lot, what not to do in hard times and what to do," she added.
Captain Lindsey Horan agreed.
"To be perfectly honest, the past two months, there is just ease, there's calmness," she said.
Asked how she had been able to so quickly get the players to buy into her approach, Hayes said: "Just love, I come from a place of wanting players to enjoy themselves, I had been at a club for 12 years where I had huge success but I was desperate to do well for this country and I am so emotional because it's not every day you get to win a gold medal.
"I love America, it made me, I always say that, it definitely made me," she said, referring to her early coaching experience in the United States.
'Repay their faith'
The process of change was helped by the retirement of influential former captain Megan Rapinoe, but Hayes also made a big call when she decided to leave veteran star Alex Morgan, a two-time World Cup winner but now aged 35, off her roster.
Saturday's triumph revealed another side of Hayes to the tough-talking, no-nonsense coach who had won so much respect in European club football.
"It has been a dream of mine to be in this position, and I thank my Dad, he was the one who pushed me to this moment to be able to come here, and coach an unbelievable group of players," she said.
"I am so emotional thinking about it. I have my Dad's necklace on, its got an American eagle, he was with me today and that helped."
Hayes was also quick to say that the gold was her way of paying back the United States for showing confidence in her early in her coaching career.
"America means more to me than most people realize. And I was a 20-year-old who'd come from a pretty stuffy society that didn't embrace the women's game and women in football," she said.
"And I went to America and they looked after me, they nurtured me, they opened doors for me, they gave me opportunities that England never, ever gave me. And I'm just so happy, so happy to repay their faith in me," she said.
Defender Crystal Dunn said she was sure that Hayes is simply at the start of a successful era for the team.
"I think it's important that we realise there is so much more that we can do and having Emma for the long whole is going to be incredible.
"She came in with an incredibly difficult task but we just embraced it. We knew it was going to be difficult and challenging in some ways but we got the job done."
