McCoist watched on as his side eased into the semis this evening courtesy of a 2-0 win away to Albion Rovers in their quarter-final replay.
However, the 51-year-old was under no illusions about his side's performance and acknowledged that they would need to play better when they face Dundee United in the last four next month.
"It was important to get the first goal and we did. After that we tried to get them to come out and open up and they stuck to their plan," McCoist told Sky Sports News.
"But we got the second goal, a great header, and it was clear for everyone to see we got the 2-0 win. We will have to play better. Dundee United are a good side, we have to be on the top of our game to meet that challenge."
Rangers would face either St Johnstone or Aberdeen in the final if they were to beat Dundee United at Ibrox.