SPFL Championship side Morton caused the shock of the season so far by beating Celtic on Tuesday night while Hearts and Hibernian were run close by Queen of the South and Stranraer.
The Gers have started the League One campaign in fine form and host Stenhousemuir tomorrow afternoon.
McCoist said: "Effectively, we're playing in a cup tie every week and sometimes you get shocks in cup ties. This week proved it.
"Although I was a little bit surprised by some of the results in midweek, it's not a real shock to the system because we, more than anyone, know what's going on in the lower leagues.
"Teams at that level do well and Morton, who are second-bottom of the Championship, had a fantastic result at Celtic Park, while Stranraer scored three goals at Hibernian.
"They are reminders to people outwith our club that the surprises which come along should be expected a little bit more.
"It will be a tough test for us tomorrow.
"Stenhousemuir scored four goals last weekend against an Arbroath side which played reasonably well against us recently."
McCoist could be without striker Nicky Clark tomorrow after he was crocked in a bounce game with Partick Thistle.
"Nicky got a sore one in the first five or 10 minutes of the match on Tuesday and I'd hope it's not too serious," the Ibrox boss told rangers.co.uk
"It doesn't look like it's the type of thing that will keep him out for too long but, as for the weekend, we'll need to have a chat with the physios about that one."