Evans, who played in United's 1-0 third round win over bitter rivals Liverpool on Sunday, is one of a number of players in the Red Devils squad who has yet to win the FA Cup, with the club's last success in the competition coming in 2004.
The Northern Ireland international also spoke of his great respect for the tournament despite its recent perceived lull in popularity.
He told the club's official website: "Everyone wants to win the FA Cup. "It's a great tournament and the last time we won it was in 2004.
"A lot of the lads in this squad haven't won it, so we've all been saying that we're desperate to win it and add it to the collection."
United are the most successful team in FA Cup history and following a fourth round draw away to Southampton, are widely expected to be there or thereabouts in the race for cup glory once again come May.