Rogers said: "The board does not choose the team, and we can only note their comments.
"Team selection is a matter for the manager, and we were delighted to hear their strong support for Brian.
"The group all agreed that he is the right man to lead us out of this dip."
Little had tried to sign a player on loan last week without success, but Rogers insists the club are fully behind him.
She added: "Even the most loyal supporters are bound to feel disappointment aqnd frustration at times like this.
"But it was reassuring to hear their loyal support for Brian. My message to the fans is to give Brian their 100 per cent support while he makes the necessary changes and gets us back on track.
"It's going to be a tough couple of weeks, and it will be even tougher for the club if we are negative and divided."