The Glasgow giants head to Glebe Park on Saturday, having beaten Brechin City 4-1 on the opening day of the season at home.
But McCoist is taking nothing for granted, telling the club's website: "We saw enough from them at Ibrox, particularly in the first hour, which indicates they are a good team.
"Like most of the teams we'll face in the league this year, you'd expect they will be stronger at home."
And McCoist's assistant at Rangers, Kenny McDowall, added: "We know we'll need to be at our best to get the three points.
"That goes without saying and whether we get them will be down to our attitude and approach."
Brechin City have added new loan signings Andy Ryan and Darren Petrie to their squad.
Steven Robb could return after missing the last two matches through injury, although midfielder Allan Walker is doubtful.
Dean Shiels is unavailable for the visitors who may also have to do without Rod Wallace, Chris Hegarty and Ross Perry.