The Latics lifted their first major trophy on Saturday when Ben Watson's last-minute header secured a shock 1-0 success over Manchester City at Wembley.
Whelan, who suffered a broken leg in the FA Cup final during his playing career, was immensely proud of his club's triumph after leading the team out.
However, Wigan are now turning their attention to the fight for Premier League survival and need to beat Arsenal at Emirates Stadium to stand a realistic chance of staying up.
And Whelan has conceded that he would be willing to sacrifice the FA Cup in order to guarantee the club's Premier League future.
"Our win was closure for that," said Whelan in reference to the injury he suffered playing for Blackburn against Wolves in the 1960 final.
"And, yes, when I led the lads out I got a little bit emotional. Then it was wonderful to see the way we played them off the park.
"I was the proudest man in football but now, if someone offered me a win at Arsenal on Tuesday instead of the cup, I'd say yes.
"It's so vital we stay in the Premier League and I'm sure most people would agree we're good enough to stay in there.
"We know what we have got to do - the players are well aware of it and up for it big style."