Sundays's victory was the Light Blues' ninth in a row as they opened up a commanding 12-point lead at the top of the Scottish Third Division.
Rangers initially struggled to adapt to life in Scottish football's bottom tier, following a tumultuous summer, but McCoist believes the confidence is back again.
He said: "Keeping the momentum is really important because I think it has an effect on the opposition as well.
"That's something we want to get back at Ibrox, we want teams to fear coming here and think there's the potential to get on the wrong end of a really poor result.
"I can see the boys beginning to grow in confidence.
"It's certainly not the best we've played this season but with victories comes a greater degree of confidence.
"That adds to the strength of the team and I feel that's the case at the moment."
David Templeton set up Lee Wallace for the opener before claiming a superb goal of his own, with a Dean Shiels strike rounding off the win.
Templeton, who joined Rangers from Hearts on transfer deadline day, has impressed since making a return from ankle ligament damage.
And McCoist believes the winger has the potential to become a fans' favourite like Rangers greats of the past.
He said: "He's still got a long way to go.
"He's rightly getting a lot of praise at the moment and he's coming good.
"Remember, he had an eight or nine week rest after the ankle injury at Annan and, to be fair, he is paying us back all right at the moment.
"I think you can see the relationship he is forming with the support, which will be very important to him.
"The supporters have always had somebody like that, whether it was a Davie Cooper or a Brian Laudrup or a Paul Gascoigne.
"They always had somebody who was a bit special to them and I think Temps has got the potential to be that kind of person."
Clyde boss Jim Duffy said: "We were up against a far superior side, there is no question about that.
"They have quality in all areas. They are at a different level from anyone in the Third Division.
"You've got to accept, if you're up against that level you've just got to work hard and be disciplined and organised and, for the large part, I think we were.
"It took exceptional goals to beat us."
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