The Third Division side defeated Elgin City 3-0 in the fourth round on Sunday and now McCoist is targeting a top flight fixture in the next phase when the fifth round draw takes place later today.
"I hope so. I don't see any reason why not," he said.
"Obviously in the two League Cup games we performed well, especially against Motherwell.
"But it's not a crime being beaten by Inverness this season, as a lot of people know.
"I wouldn't start screaming from the rooftops that we're ready for anything but an SPL team wouldn't scare us.
"The main objective was to get to the next round and we did that.
"I thought our goals were well executed and we had some good individual performances.
"The most satisfying element of it all was the clean sheet. I said to the lads before the game that Elgin score goals, they are a good team going forward.
"It was a very awkward tie so I'm really pleased at going through."