After three below-par performances against Hibernian, Hearts and Falkirk, the League One champions upped their game to ease into the third round of the Petrofac Training Cup.
Kris Boyd hit a hat-trick, Lewis Macleod and Lee McCulloch scored twice and Fraser Aird was also on target as Rangers turned on the style.
McCoist said: "We were miles better. It might be an obvious thing to say, but that was our best performance of the season so far.
"I thought we were better when we had the ball and didn't have the ball. Our passing was a lot sharper and our quality of goal was excellent, the quality of finishing was superb.
"I am delighted. I just hope that this is a start for us where we can go and continue playing with a bit more speed. We were incisive up front and I thought we moved the ball quicker than we have been doing in the last couple of games.
"I would hope that we can take confidence from that and move on."
A lack of cutting edge has been a huge problem for Rangers so far this season but McCoist's side were far more creative last night and it could have been worse for Bully Wee boss Barry Ferguson - who did not speak to the press afterwards - on his return to Ibrox.
Boyd notched the first goals of his second spell at the club and McCoist was delighted for his strike star.
He said: "He scored a hat-trick, he had one disallowed and he should have scored at the end when he was through.
"It has never been something that has worried us. Boydy is one of these players, he will always score. If you get the ball into him in the right areas he will score.
"I am pleased for him. I am delighted for him, as I am for all the lads because it was a good level of performance with some excellent goals."
Rangers will now turn their attentions back to their bid for the Championship title when they host Dumbarton this weekend.