The Championship outfit turned in a superb performance as they went toe-to-toe with Ally McCoist's side and got their rewards as John Baird netted the only goal just minutes from the end of a low-key 120 minutes.
It was little more than the Fifers deserved for a gutsy display and boss Murray was delighted to see his players rise to the occasion.
He said: "It was a big task playing against Rangers, they are a massive club and I have a lot of respect for them.
"We were the underdogs going into the game and with 17,000 of their fans it was always going to be difficult.
"But we had to have that belief and I told them that. They had a chance to win a gold medal for themselves and a cup for the club, the fans and everyone in Kirkcaldy and they have done it. I am proud of the players.
"It probably wasn't the best game of football that has been played in a final but finals are about winning.
"I told the players they had a silver medal and to go and make it a gold. Don't accept that silver medal."
Victory in the capital marks the highlight of a mixed season for Rovers that has seen them struggle in the Championship yet thrive in knock-out competitions.
Murray snapped up Baird from Partick Thistle a couple of months ago and the boss said: "With the final being so late after you qualify for the final, players can come in during the window and John did that.
"He has ended up with a winner's medal so I am delighted for him. But I am delighted for the whole squad.
"We have got a very good spirit in the team and the squad. We have had a dip in the league recently but it wasn't about the league today.
"The players were playing in front of their own fans, their own family and they were worthy of being out there."