Easdale made the appeal in the face of plans by the Union of Fans umbrella group - which includes the Sons of Struth protest group - to set up a trust for season ticket money.
It would be released in return for security over Ibrox and Murray Park.
But Sons of Struth organiser Houston responded angrily: "I know thousands, myself included, who have been to more games than the director.
"We only saw him appear at an away game for the first time at East Fife when Dave King was over pre-AGM.
"So to call on the loyalty of thousands of fans who go week in, week out, is thoroughly disgusting. It is the best advert for anyone not to buy a season ticket I have heard for a very long time.
"I have had phone calls from people who are not particularly pro-board or anti-board who are disgusted with the terminology that was used."
Houston added: "Just before the AGM, Sandy Easdale was on national television and told the Rangers supporters, Rangers shareholders, anyone who was prepared listen, that he had investment lined up.
"The AGM happened on December 18 and approximately six weeks later we had to go and get … a buster loan of £1.5million to keep the club alive.
"Now, six weeks down the line, we are being told that if we don't buy season tickets we are going to go into administration. So where is this investment we were told would come into the club?
"Plus, how can you put a business into administration when you have a man [Dave King] on the sidelines with a plan to invest between £30million and £50million? It is absolutely ridiculous."