The Premier League club have launched a full internal investigation into the incident, which came to light on Friday afternoon with Brek Shea posting a picture on Twitter.
Jones reportedly responded by damaging team-mate Glenn Whelan's car, in the mistaken belief that the midfielder had been responsible.
The Trinidad and Tobago international has since apologised to Whelan and will pay for the damage caused, and although the person responsible is yet to come forward, Jones insists he bears no grudges.
In a series of postings on Twitter on Saturday evening, he wrote: "First off for all the people saying this had anything to do with racism, I'm not endorsing that.
"Secondly, I've apologised to Glenn Whelan for the destruction of his property, for all the people that think I did Michael Owen's car, I didn't. I just posted the pictures of it, I was never involved in any of the pranks in the dressing room.
"So for all the people that think that the pig's head wrapped in my clothes was banter, great, so is the broken window.
"As far as tension in the squad, there's none. Myself and Whelan had our thrash out and he said it wasn't him so I apologised and I'm paying for it.
"As for the person who did it, no-one has come forward and apologised to me so I guess the joke was good then.
"But as I said, if you have the belly to take banter to that level, be willing to accept the reaction. That's final, no more comments."