A 1-0 defeat to Dagenham on Saturday means the Pirates are now without a win in five matches but Higgs insists the Scot remains the right man to turn around their season.
"One thing I can quash is any suggestion the players are not doing their best for Mark McGhee," he told the Bristol Evening Post. "I know there are rumours to that effect, but I have seen situations where the manager has lost the dressing room and that is absolutely not the case at the moment.
"Mark was brought to the club because we felt he was the right man to do a long-term job and that remains the case.
"I can assure them that everyone at the club is working as hard as possible to turn things around. Relegation from League Two is a frightening prospect that cannot be ignored, but I firmly believe we will climb the table.
"The last thing I want to do is destabilise the club with another managerial change. The board will continue to back Mark and the players as much as we possibly can."