McCoist, reflecting on his side's first away win in five attempts this season in the Irn-Bru Third Division, said he had "no problem" with teams adopting an aggressive approach, adding: "I would do it myself. If I'm playing against Rangers in the SFL3, the first thing I would ask them is if they fancy it. Let's see if they are up for the battle, up for the challenge.
"That's the first thing you do, because they have to prove that they're better players."
In a tough but never dirty match, Rangers had two players booked, Dean Shiels and Kyle Hutton, while Clyde had three players yellow-carded, including John Neill, who was sent off in the second half.
McCoist said: "If somebody doesn't want to let you play and is aggressive, you have to combat that. You have to at least face up to it and match it. I don't have a problem with it at all. The main problem I've had is that we've probably not matched up to it. We're maybe doing that now."
He added: "It's safe to say that every team we'll play this season will certainly be up for the game, be competitive and aggressive. That's fair enough. We must be equal to that, if not stronger than that."
Rangers won through goals by Shiels – "a top, top finish worthy of any league" according to his manager – and Lee McCulloch.
McCoist said the application and will of his players were vital to the success – a sentiment reinforced by Chris Hegarty, the 20-year-old defender making his first league appearance of the season.
"We showed we could press the way teams have been pressing us. We were a bit more physical and the whole squad knows we need to get into people's faces. That's what this league is all about," Hegarty said.
Of life in the third division, he added: "We are getting smashed all over the place and we need to go and do that to teams. We need to be a bit more aggressive as well as trying to pass them off the park."
The defender said the strike by Shiels made it a perfect weekend for the family with his father, Kenny, on Saturday guiding Kilmarnock to victory over Celtic.
Clyde rued missed chances and a daft sending-off when Neill was unnecessarily involved in a clash with Shiels.
Stefan McCluskey, who was foiled by a great save from Neil Alexander but who scorned an excellent chance in the first half, described his team-mate's dismissal as "stupid".
McCluskey also admitted he had apologised in the dressing room for his first-half miss.