Rashford made his United debut as an 18 year-old in 2016, just under three years after Ferguson had retired as the manager at Old Trafford.
The England international had been in the United academy since the age of seven, overlapping with Ferguson's hugely successful tenure, but would never work directly with the Scot.
Rashford discussed Ferguson after receiving the Football Writers' Association's Tribute award for his work campaigning to end child poverty in the United Kingdom.
Ferguson has backed the United striker and spoken to him personally, and Rashford told the FWA: "For me, it was an unbelievable experience.
"For me, that's probably the only regret I've ever had in my career: never getting the chance to play under Sir Alex. It's something that is never going to happen now.
"To be on the phone with him and just have 10, 15 minutes conversation was amazing."
Rashford did get the opportunity to play alongside United's record goalscorer Wayne Rooney, however, and was effusive in his praise of the former England captain.
"Me and Wayne are different players, we play a lot different on the pitch," Rashford said.
"But in terms of the way he showed his versatility on the pitch, he's what I would consider one of the best players the Premier League has ever seen. You could put him anywhere on the pitch and he just has that football understanding.
"There's a few other players like that, like [Paul] Scholes, where you could play them anywhere and they'll make things happen and they'll give you a good performance.
"For me, despite all the goals he scored, that's one of the things that stood out to me. At the time, I think he was playing number 10 when I first came in, sometimes midfield and sometimes as the number nine.
"I just saw the professional side of it. He was always ready to play and give his best when he was on the pitch. That probably made me mature a little bit as well, seeing how professional he was.
"I'd been a fan of his since I was a kid, watching him score goals left, right and centre, so the goals I knew he was scoring, but this side of it was new to me and I'm glad that I got to experience that."
Ferguson and Rooney were both previous recipients of the FWA Tribute award, along with Scholes, Ryan Giggs and David Beckham, three other modern United greats.
"As a kid, you want to follow in the footsteps of people you see as heroes," Rashford said.
"I know on my journey to the first team, it was all about doing the things that they'd done, making the same starts that they'd made to get into the same position that they were in.
"I've been lucky enough to be able to experience that journey and make my way into the first team like they did.
"To get this award and for them to have had it before me is an amazing feeling."
But Rashford is not done, having this week continued his work by highlighting the poor quality of free meals given to children, again forcing change.
"We're at the beginning of what I see as a long journey," he said. "I'm definitely not at the stage of relief yet; I feel like there's a lot more that needs to be done and a lot more steps that need to be taken forward."