A visibly-shaken Jones, cleared of child abuse charges in 2000, described all Leeds fans as "vile animals" after being targeted by chanting travelling supporters during his side's 1-1 draw.
The game was overshadowed by the assault of Owls goalkeeper Chris Kirkland by a visiting fan who had run on to the pitch to celebrate Michael Tonge's second-half equaliser.
Aaron Cawley, 21, from Cheltenham, was today jailed for 16 weeks and handed a five-year football banning order after pleading guilty to assault and entering the field.
Wednesday fans sang about the two Leeds fans stabbed to death in Turkey in 2000, while riot police were called on to quell violent outbursts. Both the FA and South Yorkshire Police have launched their own investigations.
Leeds chairman Ken Bates, who condemned both sets of fans, said that by choosing not to mention the part Wednesday supporters had played, Jones had lost credibility.
But in direct response Jones, who had earlier apologised for describing all Leeds fans as "vile animals", said in a statement: "While I have nothing but the highest regard for Ken Bates and his considerable contribution to football over many decades, I feel compelled to issue a response to his comments published in the local media.
"I must make it clear that had I heard Sheffield Wednesday supporters chanting anything of an offensive or abusive nature on Friday evening, I would have rightly and roundly condemned them.
"There is no place in football or society for vile chants of any nature and I endorse that view completely.
"But the abuse aimed at me on Friday was personal. It was also wrong, it was offensive and not the first time I have endured such abuse from Leeds United supporters. Why make it personal? Why were the chants aimed at me?
"I cannot emphasise strongly enough that I condemn any abuse of any kind from any supporter and I would stress that the vast majority of fans at every club in the country are decent and law-abiding.
"I have no desire to become embroiled in a tit-for-tat war of words on this subject and would now like to draw a line beneath it and concentrate on the job I am paid to do, which is managing Sheffield Wednesday."