The Light Blues booked their place in the fourth round with a comfortable 3-0 win over Airdrie at Ibrox on Friday night, with Jon Daly claiming a double and substitute David Templeton also on the scoresheet.
Rangers were well beaten when they were dumped out of the competition by Dundee United last year but McCoist believes his Scottish League One side should be better equipped to compete with top-flight opposition this time around.
He said: "It would be another test. If we get a Premiership side we will just have to deal with it when it comes.
"We've got a group of players who have had top SPL experience so I would be very hopeful we could give a good account of ourselves against a top team.
"I would take a home tie, which would be great. I think that's all you can ask for. I wouldn't start singling out teams who we would want or want to avoid.
"I don't think we are in a position to do that but if somebody could offer me a home draw I would take that."
Daly's double took his tally for the season so far to 14 goals, with seven coming in the last four games.
McCoist said: "I'm delighted with Jon. His first goal was a great finish and the second one is the type of goal you would expect from the big fella.
"It's another two goals to his tally. I know he has set himself targets and I hope he is well on the way to reaching his targets and surpassing them."
The manager also paid tribute to Templeton, who has struggled to nail down a place in the side this season.
McCoist said: "He has done well. He has come on in games and had a very good and important impact for us.
"I've spoken to the lads who aren't starting and it's difficult for them but they have to be patient.
"You have to be fair to the boys in possession of the jersey for doing well."
Airdrie were unable to play goalkeeper Scott Gallacher, who is on loan from Rangers, and brought in veteran Tony Bullock on an emergency deal.
Boss Gary Bollan was satisfied with the 41-year-old's display but admits a question mark remains over his future with the club.
He said: "We got Tony in on Friday morning and he came in and did a job for me. Whether he's going to play again, we will have to see."