The Light Blues picked up their first away league win at this level with a 2-0 victory at Clyde on Sunday - with goals from Dean Shiels and Lee McCulloch - and McCoist thinks his side are now finding their feet.
He said: "You have to match up against the opposition and let them know that you're as much up for the competitive side of the game as they are.
"It's safe to say that every team we'll play this season will certainly be up for the game and will be competitive and aggressive, which is absolutely fair enough.
"We must be equal to that, if not stronger than that."
"If I'm playing against Rangers in SFL3, one of the first questions I would ask is 'do they fancy it? Let's have a look and see if they're up for the battle'.
"The vast majority of the footballing public might think we do have better players than SFL3 but, that said, you've got to earn the right to play.
"The one over-riding factor that should always be there is a desire to work your socks off and they got their rewards because of that."