The skipper and Sebastien Faure were both caught out as Bobby Linn struck on the break to put the Red Lichties 2-1 up at Ibrox.
He showed great composure later in the second half though as he stepped up to fire home a good penalty that secured a 3-2 success against the Angus side.
McCulloch continues to be a crucial player for the Light Blues this season and his effort was his 13th counter of the campaign.
McCoist wasn't happy with the way he and his defensive colleagues played at times but was thrilled to see him respond in the right fashion.
The manager told the club website: "If I'm going to be fair, there were two or three things before Lee went in for his missed tackle at the second goal I wasn't too pleased about.
"Defensively we were all over the place there. Big Bilel (Mohsni) knocked the ball inside and that was the initial problem.
"I can guarantee you we'll be looking at the two goals we lost this morning when we meet for training.
"The skipper did well after that though and when we got our penalty with 10 or 15 minutes to go, there was only going to be one man taking it.
"Lee's record so far from the spot has been excellent. He wants to take the responsibility, leads by example and shows great nerves to do it.
"We're just really pleased he is in our side because he has been a tower of strength for us throughout the season.
"In general, it's important we get a winning mentality among the boys and a never-say-die spirit. They've definitely got that in abundance.