The 21-year-old spent six years under Sir Alex Ferguson at United before making last season's loan spell at the KC Stadium permanent this summer following Hull's promotion to the Premier League.
Despite Ferguson describing the winger as a possible successor to left-back Patrice Evra, Brady never got a real first team chance at Old Trafford and now he has revealed that turning his back on the former United manager was the right decision.
"I left United on good terms. The six years I was there really helped me as a footballer," he told the Daily Star.
"I wouldn't be where I am now if it wasn't for United and Sir Alex. I enjoyed my time there.
"This is a new chapter. Sir Alex had me playing at left-back and although I'm higher up the pitch now, I think it helped me in the long run.
"It's a big step leaving United. I didn't know anything else but them. But it was the right decision and I'm really happy. I left with Sir Alex's blessing.
"He's an inspiration, the best manager ever, and I really enjoyed my time working under him."
His move to Hull saw him play a pivotal role in Steve Bruce's successful side as they secured a return to the Premier League after relegation in 2010.
Brady believes the time was right to move on and his form for last season's Championship runners-up has seen him break into the international setup with Republic of Ireland.
He said: "It was time to move on and things are going well for me now.
"I've got myself into the Ireland squad and we have two qualifiers coming up next week so hopefully I'll get a run out in them both."
The winger helped the Tigers to their first win of the season as his penalty secured the three points over Norwich City and he believes his side have what it takes to survive this season.
He added: "It was a big win. We needed that kick-start. It shows people that we can compete at this level."