And he insists they will have some explaining to do when they address shareholders at Thursday’s annual general meeting.
With no approach made for the Aberdeen manager, both McInnes, right, and Pittodrie chairman Stuart Milne put on a united front last week insisting he had no intentions of leaving.
McCulloch said: “He does tick the boxes. It’s the AGM on Thursday and I’m sure all the questions will be answered.
“I know the fans are getting a bit impatient and rightly so. I feel sorry for Graeme Murty, who is a tremendous coach who did well the first time around.
“He has done well this time too because he is dealing with a squad which is low on confidence right now.
“The results haven’t gone his way recently, but I know he will be in every day trying to get the best out the players.”
The former Rangers skipper believes there is increasing pressure on the board to deliver.
McCulloch said: “It is important Rangers get it right this time. They went outside the box with Pedro Caixinha and it didn’t work, so it’s so important they get it right.
“They need a strong finish to the season now.
“The fans have backed the club, the board and the team and it’s time they got something to shout about. Getting a new manager in soon will help with that.”