A Ben Watson goal in the 90th minute was enough to win Wigan the trophy and it left Whelan almost lost for words.
Whelan told Sky Sports News: "I am not normally nervous but I felt emotional all day. But I had a dream. I said we'd beat Everton and then Man City 1-0 in the final. It was a fantastic dream and it came true.
"We have unfinished business though in the Premier League so there will be no champagne. We will celebrate next Sunday when we stay in the Premier League.
"We played well today and we were the better side. We played City off the park."
Wigan face Arsenal at the Emirates Stadium on Tuesday and must win if they are to have any chance of climbing out of the relegation zone.
Whelan says the season could have been so much different in the Premier League if it had not been for bad luck.
He added: "We struggled in the league because of injuries. I haven't had a dream yet either about our league destiny, but hopefully that will come tonight."