McCoist and his side have come under fire following Sunday's 1-0 defeat by Raith Rovers, which continued the manager's poor record in cup competitions.
The all-time record Rangers goalscorer has come under increased criticism, especially after photographs emerged which appeared to show him singing karaoke at a post-match function at Ibrox.
McCulloch declined to answer questions on what happened on Sunday night - but he revealed there were strong words between the players following their extra-time loss at Easter Road and backed McCoist ahead of their William Hill Scottish Cup semi-final against Dundee United at Ibrox on Saturday.
"The dressing room are right behind our manager," McCulloch said. "He has been there through thick and thin for us, and for me especially so.
"We have got Saturday to repay the faith the manager has shown in us, and repay the fans and give them something to shout about.
"We definitely owe the fans, the way they have turned out, and we feel we really owe the management team. The way the supporters filled the stadium, to let them down doesn't feel the best."
McCulloch was speaking at the launch of the club's season ticket renewals, a deadline for which has been set for May 6. The club's 120-day review of finances, a crucial factor in many fans' decision to renew or not, finishes on April 17
The club have put up most prices by about 15 per cent, with some up more than 20 per cent, although some child tickets have been cut to £50 and "value" season books are available in one section for £250.
McCulloch was keen to look ahead to the semi-final rather than reflect on the shock defeat, but he said: "We missed a few chances and they had a little bit of luck at the goal with big Bilel (Mohsni) slipping and the rebound falling to their player. But we did more than enough to win the game - we just couldn't put the ball in the net.
"We had a meeting and we are bitterly disappointed obviously. The only thing I can say is it's gone now and with such a big game coming up on Saturday, we need all our energy and focus to hopefully get to that final.
"As players, we are an honest enough bunch. We spoke with each other and ironed out a few differences, so to speak.
"There is definitely fight in the team. The management is installing fight in the team. But last weekend we let everybody down. The boys are more than aware how important this game is."
The 35-year-old accepts that criticism is inevitable when Rangers are knocked out of cups, but he believes everyone can handle it and bounce back, including McCoist.
"He's a big boy, he knows, as the players do, that last weekend's result will bring criticism," the former Motherwell and Wigan player said.
"I've had it myself, the manager has had it, and the players have had it.
"The players, more so, deserve criticism for not winning a game we felt we should have won."
The League One champions have been accustomed to winning for the vast majority of the season but McCulloch feels the new players that came joined last summer will cope with the disapproval.
"The ones that have come in have been superb, off the pitch as well, quite headstrong," he said.
"They got a wee bit of a fright when we drew a home game, at some of the criticism. So they were half-expecting it from the result last weekend. They will be ready to bounce back, we have some strong characters in the dressing room."
However, McCulloch believes United are favourites to reach the final and he claimed the game was "not a home tie".
He explained his reasoning: "The results they have had, the form they are on, they have some really good players, albeit so have we.
"I'm not underestimating us, I just think they are favourites. I've not checked but Dundee United, I would imagine, are bookies' favourites."