Quinn, who also played for and managed the Black Cats, watched on as Di Canio replaced Martin O'Neill and presided over a stormy reign before being dumped in favour of Poyet.
The Irishman has praised owner Ellis Short for remedying the Di Canio problem, though, even if Poyet was not his ideal choice for the job.
He said Poyet - in the wake of the win over Manchester City - had got the team playing "beautiful football", and backed him to continue his progress.
Speaking as he received the honorary Freedom of Sunderland at a ceremony at the Civic Centre, Quinn said: "You cannot predict football. If anybody said, outside Sunderland, that they were going to beat Manchester City 1-0 again, you would have laughed."
Poyet is in the job because both O'Neill and Di Canio were deemed to have failed, and Quinn added: "When I left I did feel Martin O'Neill was the right man and it would go from strength to strength, and I am as puzzled as any Sunderland fan as to why that relationship - Martin O'Neill and Sunderland football club - isn't still going and isn't thriving.
"The Paolo Di Canio thing, we now know, was a debacle in many respects.
"Everyone will remember the Newcastle result (a 3-0 win). But it was not to be.
"I don't know Gus Poyet but I think if I had been at the club I don't think Gus Poyet would have hit my radar as strong as it did Ellis Short.
"From the outside looking in I really like what I see. I am more than pleasantly surprised. He has a real thirst and vitality that he wants to make this work. It's very important that he is buying into the region, like I did all those years ago. I like that.
"But I also like the way he has a team who are down at the bottom of the league, supposedly doomed to relegation, all the fears in the world should be there, and they played some beautiful football yesterday against Manchester City.
"Wes Brown was an inspiring leader to come back in and do what he did after 22 months out. It tells me there something good happening in the dressing room."
Short has not hidden from the responsibility of hiring and firing Di Canio - never a trouble-free choice to start with - and Quinn has praised him for standing up to take control.
Quinn said: "(He deserves) a real pat on the back for doing what he did so quickly with the Di Canio situation and bringing someone in like Gus Poyet.
"I think the future bodes well. You feel the impetus is there and they can go and play teams now with so much less fear and enjoy the games.
"If Gus Poyet manages to do it and pulls it off (keep Sunderland up), I think it is one of the best things to happen to the club in many, many years."
Quinn, who signed for Sunderland from Manchester City in 1996, said he was flattered and humbled to receive the Freedom of the city.
He added: "It has been an incredible time from the moment I first came up.
"My children were reared here, they are still really strong Mackem, Sunderland fans.
"It will always be a special place for me, a place which meant more to me than anywhere in my career."