The Glaswegian is approaching his 25th year in charge of the Manchester club and Dublin admits that his broken leg enabled the Red Devils to acquire Eric Cantona.
He jokingly told ESPN Classic: "It was my Old Trafford debut and it lasted about 60 minutes and my left leg and left ankle sort of gave way on me from a tackle from behind.
"I am the reason why Man United have won all those trophies - its down to me, it really is. I break my leg and then they bring in this has-been called Cantona who just takes the world of football by storm!
"As soon as he came in it just took off. Players warmed to him. Eric is bigger than me: 6ft 3in or 6ft 4in - he had a touch of a genius, he could head it, he could tackle, left and right foot, the guy was an absolute genius. And I think that’s what Man United needed."
Dublin also revealed Sir Alex's half-time team-talks are highly motivational, despite the Scot having a reputation for dishing out 'the hairdryer treatment' at a poor performance.
He continued: "Some people need the hairdryer.
"I had it and I don’t even know where I was. The only thing I remember about it was we were playing against a team in red and white stripes and I had a stinking first half, missed a load of chances and he was right there at half-time, told me what he thought. I went out and scored a goal in the second half.
"I respect the man for knowing what kind of character I was to get the best out of me."
But the striker turned serious when talking about the Scot's man-management style, and Dublin believes the former Aberdeen boss knows exactly how to handle different personalities in the dressing room.
He added: "What he does he looks after people like Cantona, people like Ronaldo. They’re personalities that you can’t just treat the same as you would treat me or you would treat Lee Sharpe or Gary Pallister. Because they’re all different characters so some people need an arm round them, some people need the hairdryer.
"You know if you do that to Eric he would have just left. Do it to Ronaldo then he’d have just left. So you’ve got to know how to do that and Sir Alex is the best at it."