The game at Kingsmeadow was called off after just six minutes on Sunday as players repeatedly slipped on the frozen surface.
It had kicked off as scheduled following a pitch inspection by referee Paul Howard.
“We have to say that it’s time for undersoil heating,” Hayes told the BBC. “We have got to take our game seriously. Yes we can have blowers and little pitch tents but it is not enough.
Hayes added: “It is not for managers to decide if it is on, it is up to the FA and officials.
“Everybody wants to get the game on. But when you have got emotions, of a team wanting to play or a team not wanting to play, that is why you have to have outsider parties there. But there is no FA here, and they need to be at our games to executive those decisions.”
Former England and Brighton manager Hope Powell said the situation was “embarrassing” for the game, while Chelsea midfielder Erin Cuthbert said she was "angry and frustrated".
England Arsenal forward Beth Mead said the situation was "not good enough", while her Arsenal team-mate Vivianne Miedema said: "FA and clubs, please do better."