The Rangers boss is hoping his side can build on last weekend’s win, which took the Light Blues top of the table, when they face Clyde on Sunday.
He said: “I’m getting sick of my own voice saying ‘it’s high time we got an away victory’ and we need to start on Sunday.
“It’s not going to be easy because of the level of competition we are facing, especially away from home.
“It won’t be new to us, it will be exactly the same but we have to match that as I keep telling everyone I believe we have better players.
“However we won’t get anything unless we match Clyde on Sunday and I think we’ll do that.
“We’ve had them watched a few times so we know what to expect and I’m very hopeful we’ll get our first away win in the league.
“I’m looking forward to the day when we don’t talk about it anymore. I can totally understand the interest from the media and the disappointment from the supporters.
“If we can manage to get a victory I’m not sure it will put everybody off the scent but it would certainly help us in our challenge to get out of the league.
“I wouldn’t say too much has been made of it because it has been disappointing.
“The main objective is to win the league and get out of the division but at the same time we want to do it with a bit of style if possible.
“We haven’t done that. It’s certainly not something we’ve been playing with away from home and we know that and we know what’s expected.”
McCoist is hopeful that his side’s move to the top of the table thanks to victory over Queen’s Park last weekend will give them something of a psychological lift.
He added: “I said after the game that I hoped that was a mental block that we’ve overcome and the next one, in an ideal world, would be an away victory.
“These are all steps that we have to take to get out of the division and last weekend was a good day for us with a clean sheet, a win and going top of the league.”