Furneaux has responded by saying that Boulding should question why Groves was sacked and the part he played in the sacking.
"I was disappointed to lose Michael because he's been a constant part of the side," Furneaux told the Sports Telegraph.
"But he has also been in the side during the run that has led to the manager leaving. It was obvious that we had to change things.
"People were calling for change and we changed it.
"But Michael was part of the side that underperformed. No-one has pointed the finger at any one player but everyone has to take responsibility for Paul Groves' going."
Furneaux also added that he managed to get more money than what was required to release Boulding by delaying the transfer and threatening to appeal to the Football League.