Keith Curle was dismissed earlier this month after less than a year in charge at Meadow Lane.
County's development squad boss Chris Kiwomya was handed the caretaker role, making him their 10th manager since 2007.
"I am just sick of it now," Judge told BBC Radio Nottingham. "I have only been here two and a half seasons and that is my sixth manager.
"I don't know what is happening to the stability they want to have. They have to stick with it. Eventually they have to stick with the manager. They cannot keep doing it."
Chairman Ray Trew said a combination of poor performances and falling attendances was behind the decision to sack Curle, but Magpies skipper Neal Bishop has backed Judge's call for stability.
"In three and a half years I have seen off 10 managers. We were in an indifferent run of form, but overall we felt we were on the right track. The players are all disappointed.
"We could see we had had the right man in charge. Some people had said the manager was too close to the players but that's a load of rubbish; he was hard but fair.
"I have seen Judgey's comments and I fully support him. But we are professionals and we have to get on with on it."