A newspaper report earlier this week claimed chief executive Charles Green had asked Ally McCoist to consider removing assistant manager Kenny McDowall and first-team coach Ian Durrant from his backroom team. The Light Blues boss later said no discussions had taken place with the Ibrox chief over the duo.
And, having delivered the Irn-Bru Third Division title this season, McCulloch was keen to pay tribute to the work of the three men as the rebuilding job at the club continues. He said: "Of course they are an integral part of going forward. From where the club was just over a year ago to today, we are much better off and that's the main thing.
"As players, we are behind the coaching staff. We have come a long way with them. We work hard with them every day. We go out to win on a Saturday for them, for ourselves and for the fans."
McDowall stepped in for McCoist at Friday's pre-match briefing ahead of the visit of Clyde. But he refused to be drawn on whether he had any doubts over his own role at Rangers, saying only: "I've not got any comment to make on that."
The Rangers number two was also tight-lipped when quizzed on recent headlines relating to off-field issues. Former owner Craig Whyte has claimed he was involved in the new company that took control at Ibrox last summer - months after his actions plunged the club into administration.
Green then found himself in hot water with the Scottish Football Association for allegedly breaching rules in relation to "offensive and racist comments."
Asked if Rangers' reputation had been dented over the last couple of weeks, McDowall replied: "It's not really my position to comment on that, I'm here to comment on the football side of things. We're delighted we've got to this stage of the season and we're 24 points ahead. We've got a game at home against Clyde that we are looking forward to."
The title may be in the bag but McCulloch has admitted Scottish football's bottom tier was tougher than anticipated. He said: "It's definitely been harder than we thought it would be. Not being disrespectful to teams, but I think the expectation levels were that we were going to win 4-0, 5-0, 6-0 in every game.
"We knew that wasn't going to be the case but we thought we would have played a little bit better in some individual games. There are a lot of youngsters in the dressing room, in the squad. People will say it's the same average as teams like Dundee United but it's different playing for Rangers. The young boys are playing in front of 48,000 every second week and, believe me, it's much, much harder."