Killie fans have threatened to shun season ticket purchases following the sacking of manager Kenny Shiels but Bradford City's Nelson, who departed Rugby Park in January, has advised them against that notion.
"I can understand the supporters' reaction to Kenny's sacking. You only have to look at what he did as manager," Nelson told the Daily Record.
"He courted controversy all the time with what he said but that was part of his charisma and made him the man he is.
"The fans loved Kenny so much because he protected Killie and was not afraid to stick up for the club.
"If the supporters carry out their threat, it would not be good for the club. That will only affect their ability to attract new players.
"The club have now sacked Kenny, and fans are threatening to boycott buying season tickets and the club merchandise until Michael Johnston (club chairman) is removed.
"It is such a shame to see the fans turn on the chairman although I can see both sides of the arguments.
"But there are no winners when there is internal turmoil and strife at a football club.
"I just hope any conflict of interests gets sorted in time for the new season and Kilmarnock get the chance to move on."