The Edinburgh club have not won the competition since 1902 and will be hoping to bring their 111-year wait to an end when they face Celtic at Hampden Park.
Fenlon 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."
Hibs have had a difficult route to the final and Fenlon 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.
"We've had to fight for the right to get here and we don't want to give that up too easily now that we've got there."
Hibs lost 5-1 to Hearts in last year's Scottish Cup final but Fenlon said: "Forget about it!. It's a completely different game, it's a completely different squad as well."