The Light Blues were emphatic winners as they thrashed Airdrieonians 6-0 at New Broomfield on an evening when they could have won by a much greater margin.
Andy Little, Nicky Law and Jon Daly were all on the score- sheet during a thrilling victory in Lanarkshire. But McCoist took heart from seeing Lewis Macleod and Robbie Crawford find the net, too, in a rousing success.
The expectation from many is that with more experience in general, the majority of the manager's summer recruits will become fixtures in the team.
But the likes of Macleod, Crawford, Sebastien Faure and Kyle McAusland are all presenting good cases for inclusion in the first eleven in their absence at present.
McCoist told the club's website: "I think competition for places is imperative, more so at this club than any other because of the competition we face from other teams.
"We've thrown down the gauntlet to the boys who are in the team and we've asked them to go and make it difficult for them to be left out.
"That's what they are doing. Robbie and Kyle, after not getting to grips with things on the right in the first half at Airdrie, were excellent in the second.
"Robbie chipped in with a goal and was doubling back while Kyle was going in for headers with Martin Hardie, who is six feet two, and winning them.
"All of these boys know it's going to be difficult for them to stay in the team, but hopefully that's going to keep them on their toes."
McCoist has seen his team win its first three SPFL League One games of the season with 13 goals scored and only one - Steven Jackson's stunning overhead kick for Brechin - conceded. He has urged caution and doesn't want people to get too carried away with the strides his players have taken.
But he admits things are shaping up well and added: "It has been much better and we're certainly better placed than we were 12 months ago.
"Last year we managed to win the league by 24 points and we are indebted to everyone in it for that.
"Although it wasn't a fantastic start to the season then, it should never be forgotten that they won Rangers a title in the end.
"We've started a lot better in the league this year but we've still got miles to go. That said, it was very, very encouraging against Airdrie."