Bilel Mohsni, Jon Daly and Lee McCulloch all scored as the Light Blues wrapped up a 3-0 win over holders Queen of the South at Palmerston.
Rangers are a league below Jim McIntyre's men, but they have made a fine start to their League One campaign, with five straight wins.
McCoist admits a cup success would be a bonus, however, he is fully aware that failure to clinch the League One crown could cost him his job.
"It would be great to win the Ramsdens Cup but we want to win every cup we're in," he said. "We were gutted last season to be knocked out of it by the team we beat tonight.
"The one I want to win is the league because I won't be in a job if I don't get us promoted. But I want to win every competition we enter and we're still in the Ramsdens and Scottish Cup this season."
Chris Higgins' dismissal for a second booking opened the door for Rangers to add two more goals, but McIntyre took plenty of positives out of the game.
"The sending-off was pivotal. It was Higgins' man who scored from the free-kick," he said.
"But I've got nothing but pride for the players because we really took the game to Rangers. They were ruthless and scored their first chance and we didn't have that side to us."