Weston stamped on Warrington's face after following through in a tackle to win the ball at the Priestfield stadium last Tuesday night, leaving the Millers 'keeper needing ten stitches to three deep gashes.
Boss Ronnie Moore exchanged words with counterpart Andy Hessenthaler at the time who has since defended his player, but the Millers are unhappy the referee allowed the incident to go unpunished.
"If it was a 50/50 tackle, I would stand up for everybody but when it is in the goalkeeper's hands you cannot hit him on the head. I'm going to go as high as I can and let everyone know that we are still not happy with the situation", said Moore in the Star.
"I don't see why we should be treated any differently to the Premier League boys if we think there is something not quite right. If he had done that on a Saturday night he would have been locked up."
Chief Exec Paul Douglas added: "We are asking for clarification from the FA and the referee's department on how this escaped a red card.
"Having had the opportunity to review it on video, it was clearly a reckless tackle. There was no way the player was going to win the ball and there was little regard for Andy's safety when he went infor the challenge. It should have warranted a red card.