WalesOnline has reported that members of staff did ask the centre-back whether the goal was deliberate, and Hudson has admitted that the accusations were upsetting.
He said: "I've made mistakes, I've scored own goals before, but I've never had someone at the club accuse me of putting the ball into my own net on purpose.
"It wasn't the manager, but what was suggested is not something you want to hear at all. So that's what that tweet was all about."
After his transfer to the Terriers had been completed, Hudson tweeted to thank the Cardiff fans for their support during his five-year stay in south Wales.
Hudson had captained the club since his arrival in 2009, and led his side out in the 2012 League Cup final and during the 2013-14 Premier League season.