Minutes before the Steelmen's Scottish Cup fourth-round replay win over Hearts at Fir Park on Tuesday, McGhee learned he had lost out to George Burley for the Scotland manager's position.
The 22-year-old believes Celtic and Rangers fans, who are enjoying an engrossing battle between their clubs for the Clydesdale Bank Premier League title this season, would love the former Wolves and Leicester boss to be in charge at their club.
He said: "It's definitely a boost that the boss is staying. It's also a boost that the two Old Firm bosses are top drawer.
"If any of them had to go then we would be worried.
"Ask any Old Firm supporter and they would like Mark McGhee in the hot seat.
"But luckily Walter Smith and Gordon Strachan have been there and done it and we are just glad those positions are filled.
"As far as we are concerned Mark McGhee is our manager. I don't know if he would have wanted to take care of Scotland on and off because he gets right into training, he's there every day wanting to be involved.
"That was what I was counting on."