Stubbs could hear the laughter when he claimed Hibs would win the Scottish Cup but he was proved right when his team took the trophy back to Leith for the first time in 114 years.
The former Hibs boss felt the attitude of players and fans transforming during his two years in charge, culminating in that famous victory over Rangers in May 2016.
And he is sure his successor, Neil Lennon, will be drumming into his players that they can end Celtic’s 59-match unbeaten domestic run when they meet at Hampden in the Betfred Cup semi-finals on Saturday.
Speaking on behalf of BT Sport, Stubbs said: “The impact of that game, whenever they come back to this stadium, they will always have a positive experience of that day. And that will be a real boost to them on Saturday - they know they can come here and win.
“Before that there was always an element of doubt. It was as if ‘oh, we’re back to Hampden, we’ve had some bad results here’.
“Whereas now, the whole club has gone to another level. It’s been a huge transformation.
“When I first went in, it wasn’t just the players that thought that, it was the fans as well. We had to change the mindset, that we were going there to win.
“With the Scottish Cup, I always said: ‘They are going to win it sooner or later. Someone is going to be sitting in this seat one day saying I am the man that won the Scottish Cup for them’.
“To be honest, whenever we were in press conferences, there was always a chuckle and a little bit of doubt from reporters who said ‘we have heard it before’.
“I get that, but someone was going to do it and I was lucky enough to be that person.
“Targets and stats are always there to be toppled. Sometimes you have got to be patient – 114 years was a long time but it was well worth the wait.
“Celtic’s run is the next one now in Scottish football that’s going to go. Whether it’s this weekend, only time will tell. But Hibs will have a good opportunity to be the ones that do it.”
Hibs have already come as close to any team – John McGinn putting them 2-1 up at Parkhead last month before Callum McGregor earned Celtic a point.
Former Celtic skipper Stubbs said: “It’s going to be difficult but I do think they have got a good chance of doing it. Someone has got to stop the run sooner or later. It can’t carry on.”
• Hibs v Celtic is exclusively live on BT Sport 1