The Latics had never gone beyond the quarter-finals of the competition before this season but a remarkable story ended in perfect fashion when substitute Ben Watson headed an injury-time winner.
Whelan bought Wigan 18 years ago when the club were in the bottom tier of the Football League and struggling to attract crowds of 2,000, and Saturday's 1-0 victory earned his club the first major trophy of their 81-year history.
Not many people predicted the outcome that played out on the same stage on which the chairman broke his leg as a Blackburn player in the FA Cup final of 1960 - but Whelan did.
The 76-year-old, who led the team out, said: "I'm not normally nervous about anything, but when I went out I did feel emotional. I was only 10 yards away from where I broke my leg.
"But the dream I had that I told everyone a fortnight ago when we played Everton that we'd beat Everton, then we'd get Blackburn Rovers in the semi-final, well we got Millwall instead and we beat them, then we'd play City in the final and win 1-0.
"I did predict all this, and it was a fantastic dream. It was a lovely dream that night, and it's come true."
Wigan matched last season's Premier League champions throughout the 90 minutes, with Callum McManaman particularly impressive on the right, and it was the forward who forced Pablo Zabaleta into the two fouls that earned the City full-back a red card.
Still it looked like extra-time would be necessary only for Watson, who had been on the pitch for 10 minutes, to head in Shaun Maloney's corner.
Whelan said: "We played so well. Manchester City are a quality side. I thought we were miles the better team. We should have had a penalty just before half-time. We had more chances and we played them off the park.
"We've only struggled in the league because we've had so many injuries, we've had really bad luck. We're a small club so it's difficult to replace those.
"You could see the pride in all of our supporters that we'd won the cup and will take the cup back to Wigan. All we want now is for the rugby league team to bring the Challenge Cup back to Wigan and Wigan is back on the map big style."
There will be no celebrating just yet for the Latics, though, with their Premier League future still very much in the balance.
Three points adrift with only two games left, Wigan travel to Arsenal on Tuesday before a potentially huge game against Aston Villa at the DW Stadium next weekend.
Whelan said: "We have unfinished business. We've got a match Tuesday and a match Sunday. The lads are going straight back, there's no celebrations. They're in training tomorrow [Sunday]. We celebrate when we stay in the Premier League on Sunday night."
It would be a remarkable escape even by Wigan's standards - but Whelan and manager Roberto Martinez have no doubts it can be done.
The chairman added: "I've not had a dream on that but I hope I have one tonight [Saturday]."