Competition rules restrict the use of trialists beyond the first round, meaning new recruits Jon Daly and Nicky Law - who both netted against Airdrie on Friday - are ineligible for the visit of the Wee Rangers.
The Light Blues must wait until September 1 when a transfer embargo is lifted to register their eight new players.
McCoist said: "I've got one or two concerns but there is nothing I can do about it.
"We just have to go out and prepare right, which we attempt to do for every game, and treat the opposition with respect.
"It's up to the boys who go out and play the game.
"It's not ideal because of the circumstances in terms of the personnel we are allowed to pick from.
"But that's where we are and we just have to get on with it."
McCoist is keen to see his side go all the way in the Ramsdens Cup this year after suffering disappointment last time.
Rangers were dumped from the competition by Queen of the South on penalties last year and will face the Palmerston Park outfit in the next round if they progress past Berwick this time.
McCoist said: "We are expected to do our best - and we expect to do our best - in every competition we are in and give everything we've got.
"The Ramsdens Cup is no different.
"Queen of the South put us out last year and we want to do well in the competition this year.
"We want to go all the way. It's no different from any other competition.
"No team has any divine right to win any competition.
"But we always go into any competition and do our best to win it and we expect to do well and do our best for the fans.
"That's what we will do again."