Danny Lennon's side will take on the Hoops in a semi-final clash at Hampden next weekend, but before that Imrie wants the team to keep their minds firmly focused on Saturday's tie with Ross County.
He said: "I don't think the manager will allow anyone to have their thoughts on the League Cup tie."
"Obviously it's a big game for us and everyone wants to be involved in it, but the best way to do that is to impress against Ross County. We are all feeling the benefit of the break that we got, but we know that this is where the hard work starts again.
"The cup games are great to be involved in, they give everyone at the club and in the town a lift, but the bread and butter comes down to what we do in the SPL.
"That is where we know that we have to strive for some consistency and try to keep the results that we had over the festive period coming."
It has been a staccato season for Imrie, who has been in and out of Danny Lennon's starting XI.
He admits that it has been frustrating at times, but is optimistic there will be a fresh slate this week following the short winter break.
With the club gearing up for a push into the top six, Imrie is desperate to cement his own role in the side.
"It is obviously difficult when you aren't as involved as you would like to be," he admitted. "It isn't something I have ever really had to get used to before now in my career and it has been hard to take.
"But it is a relatively small squad, and over the course of the season everyone will be involved at some stage of the campaign.
"It is up to me to show that I am good enough to get in and stay in."
Saints were blighted by injury problems in the opening half of the campaign, with Paul McGowan out for a substantial amount of time after a shoulder operation and Kenny McLean also spending a lengthy period on the sidelines.
Given the small size of Danny Lennon's squad, St Mirren can ill-afford to be without other key members of the team for the latter half of the season.
"Obviously you want to have all of your players available but I would be wary of thinking that it is one or two players who make up the side," he said.
"We have players here who are hungry and who are good enough to play. The reason why we have fared so well as a team is because we have a good team spirit and a good togetherness.
"It is important that whatever the season throws at us in terms of injuries and suspensions we are capable of riding it through.
"There are a lot of players here who are desperate to secure a regular starting place.
"We have enough quality within the squad, whatever happens, to think that we are good enough to finish in the top half of the table.
"There are a lot of teams of similar standard in the league and what it comes down to is finding a bit of consistency."