He told Sky Sports afterwards: "I thought the second half, I thought Rangers were terrific, I really did.
"They came out of the traps, they did effectively exactly what we asked them to do second half and we had numerous chances and I felt ran out deserved winners."
"I couldn't believe it (McGregor's howler) but we did mention at half-time that if anybody deserved a break, it was Allan McGregor," added McCoist.
"You know because you only have to look at last season how vital he was in our championship winning team, saving penalties here and making numerous, numerous saves.
"So if anybody deserved a break from the rest of the lads, it was Allan McGregor and we asked the lads to go out and give Allan that break in the second half and they certainly did that."
However, McCoist refused to get too carried away at this early stage of the season.
He added: "It's the first Old Firm game of the season and it's a great result for us. That's all it is - there's miles and absolutely miles of this campaign to go.
"There'll be lots of twists and turns between now and then obviously but it is a big three points and a deserved three points."