The Edinburgh club have not claimed the silverware since 1902 and will be hoping to bring their 111-year wait to an end when they face Celtic on Sunday.
Hibs' lack of success in the competition has become something of an obsession for their fans, who are desperate to see their team finally triumph in the end of season showpiece.
Fenlon had to deal with similar talk about their record in the tournament ahead of last year's final defeat to Hearts and he knows the only solution to the relentless debate about their form in the Scottish Cup is to defeat the Hoops.
He said: "The only way to stop people from asking the question is to win it. It's as simple as that.
"It's the only way to put it to bed and we've got to try to do that.
"We can't do anything about what has gone before but we've got a great chance and that's something for myself and the players to embrace and enjoy."
Fenlon's men came through a difficult road to Hampden in order to book their place in the final and he wants them to cap an impressive run with victory over the Scottish champions.
He added: "We've had a really tough run to get to the final.
"In every game we've played, we've had to really scrap to get through, from the Hearts game, to Aberdeen and Kilmarnock, and the semi-final against Falkirk was a very difficult game."