Kenny is alleged to have sent mocking messages to QPR chairman Tony Fernandes and technical director Mike Rigg about the performance of Rob Green's performance during their 5-0 opening-day defeat to Swansea City.
In his column in The Independant, Warnock sought to clarify the situation.
He said: "As I'm sure you are aware, my goalkeeper has been in the news in relation to some text messages he exchanged with people at QPR. I have to say I was disappointed that something that began in good humour got out of hand.
"I've spoken to Paddy Kenny and he was full of remorse and couldn't apologise to me quickly enough.
"I've obviously fined him and he has agreed to finish on Twitter with immediate effect. I've also spoken to Tony and told him I honestly believe there will not be a repeat. We ended the call on good terms."
Kenny made his Leeds debut against Wolverhampton Wanderers last weekend after leaving Loftus Road earlier this summer.