The 25-year-old stormed into a two-set lead before the world No2 responded to level the match, but Murray held on to complete a 7-6 (12-10) 7-5 2-6 3-6 6-2 victory in a mammoth four hours and 54 minutes.
The Manchester United manager was sitting with Murray’s camp at the Arhtur Ashe stadium, and the 70-year-old revealed he felt more nervous than at a typical Premier League match as he watched his compatriot battle to a first Grand Slam crown.
“I’m really proud for the boy after the hard work and his progress,” Ferguson told BBC Sport. “He’s really a top player and when he really needed to show it, he showed it.
“That was a real test of a champion for me. It was a privilege [to be at the match]. I love tennis, I love watching tennis and to be involved tonight was a really special moment.
“It was more nerve-wracking than a Premier League match. I’m usually in control of my own situation but I wasn’t in control tonight.”
Meanwhile, Murray’s coach and eight-time Grand Slam winner Ivan Lendl insisted the Scot could go on to win more Majors following his success at Flushing Meadows.
“Hopefully, we’re not anywhere near where Andy can get,” said Lendl. “I didn’t come here to have a good time – I came here to help Andy win. He did, so it’s job done.”