He stressed that winning the league and – if SFL clubs reject plans for league reconstruction – promotion is their top priority this season.
He is hopeful they can get back to winning ways in their derby match with Queen's Park on Saturday.
He said: "I would be really concerned with the cup defeat if we weren't in a good position in the league. That is where we have to be judged.
"We have to improve, regroup, win the next league match. Cup runs are nice, but they are not the most important thing to our club in the next three or four years.
"Our main objective at the start of the season was to win promotion from the league. The players will certainly know it is their duty to ensure the games from now on are not flat.
"Our fans have been absolutely fantastic and they will not allow any flatness or any flat atmosphere within the grounds that we go to."
Meanwhile, McCoist has vowed to work with midfielder Ian Black to improve his discipline.
He said: "Ian is the type of character who does get caught up in things. He doesn't do himself or the team any great favours with the things that he does.
"But the other side of the coin is that he is really passionate and wants to do well. I think we can channel it and hope he does a little bit better."
McCoist has admitted he is struggling to attract new players to Rangers.
He added: "When the time comes that we are allowed to bring players to the club we are not, sadly, going to get the quality of player who will get us back to being a top level team because of where we are playing."