Both tasted action at Wembley.
Williams said: "It's unbelievable, it's what you dream of as a kid and now it's come true - winning a Wembley final."
Williams and club captain Monk, who refused to accept the armband when he went on as a second-half sub, collected the trophy together.
Monk grinned: "I generously allowed Ash to do it with me!
"It's about the journey we've been on as a club for 10 years. In the centenary year, to bring a major cup back puts the icing on the cake."