The Australian international, a former Whites player, reacted to Bates and chief executive Shaun Harvey's supposed snub before the Championship meeting between the two clubs when he blew kisses and waved to the pair after scoring at Elland Road.
Bates has spoken out about Kilkenny's behavior, indicating that it was not a shame the club lost him in the summer, and suggesting he may take a complaint to the FA.
"He can't justify or excuse his behaviour. It shows exactly why we aren't sad to see him go," Bates said in the Yorkshire Evening Post.
"Neither myself nor Shaun ever goes down to see the players on match days. Why would we?
"The fact is he asked for a wage which we didn't think he was worth. He's a petulant sod with big ideas of himself.
"We might report his behaviour to the Football Association because we've got CCTV footage of it."