A number of players and Parish himself have received messages filled with expletives in recent weeks - particularly following the defeat to rivals Brighton.
He told the Croydon Advertiser: "These people are giving our club a bad name. It's a tiny minority of fans who ruin it for people and cause problems, and they expect me to accept it.
"Well I'm not going to accept it. If you come on Twitter and call me this and that, you're going to get banned.
"If I know who you are, you're banned from the ground until you learn how to speak to people properly.."