"I remember Lee being the first person to say he was staying in the summer and it's no coincidence that he's now a major player for us now," McCoist told the Daily Record.
"We'll desperately need him in the coming months. When he made the decision, it gave the fans a bit of hope and something to latch on to.
"They needed something like that and, along with Lee Wallace, it gave the staff and supporters a real boost when the lads said they wanted to stay.
"Lee is a perfect example of someone who has taken on responsibility this season.
"All the older ones have, like (Neil) Alexander, Wallace and even Emilson Cribari in the last few weeks, but McCulloch has stepped up to the mark and he's not surprised me in that."