Paul Baker says affairs at Cheltenham are the most difficult they have been since he became chairman in 1997.
Town are 20th in League Two and manager Martin Allen is on gardening leave.
Baker told BBC Gloucestershire: "It's been a very trying few weeks. Results have not been great, and then we've got the latest developments.
"For myself and the board who have steered the club through some pretty successful times this is as tough it has been."
He added: "The club is bigger than anyone, and the fans must remember it's their club. We need them to get behind their team."
Assistant manager John Schofield will take charge of the Robins for Saturday's game at Port Vale.
"It's been a very sombre atmosphere, especially Tuesday when things happened, said Schofield.
"The players in the industry we're in quickly become hardened to change so at this moment in time we're just focussing on getting a positive result on Saturday.
"There's been no lack of effort or commitment from the players and nor should there be - they've got the best job in the world.
"Stepping up - it's part of what's expected of you and I've done it before so I'm ready and prepared for that.
"I'm being asked to do a job, that's all I'm doing and will continue to do until I'm told otherwise."
Baker added : "Football is turbulent. You never know what is going to happen. When we appointed John, we were impressed with what he had to offer, and now we're fortunate to be able to hand the team to someone of his calibre.
"I think we're in a good pair of hands for the time being until the situation is resolved, whichever way that is."
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