The Glasgow giants have endured low-key starts to their respective campaigns at the opposite ends of our game, with a lack of a competition mooted as one of the reasons.
McCoist said: "It is one of those things we will never know, but I can understand the logic in some people thinking that.
"It is probably an indirect attack on both clubs for not being professional enough in their business. We are both big enough to handle that.
"I do understand the logic in it because there is an automatic perception throughout the country that both teams will automatically win their league.
"It is certainly not from within our club, we can't allow that to happen, but I can understand the vast majority of the public thinking that.
"Maybe there is a bit of a mindset from within the club, the players, the supporters and it does filter through. I certainly hope that is not the case and I will be battering it through to the boys."
McCoist has revealed Annan's plastic pitch played a part in the horror injury that has sidelined winger David Templeton for several weeks after he sustained ankle ligament damage.
He said: "The doc said the pitch did play a part in it, but I don't know how much the surface played a part in it.
"I was out on the pitch before and, as those surfaces go, I thought it looked alright.
"Whether we should be playing on them is a completely different argument."