The duo were quick to ignore each other on Saturday after the Reds cruised to a 5-1 victory at the Amex Stadium.
Klopp appeared to ignore Hughton on the touchline, prompting an angry response from the former Newcastle boss.
However, the former Borussia Dortmund manager apologised afterwards and Hughton has tried to quash any fall out rumours.
He told the club’s official website: “Credit to Jurgen, he came looking for me afterwards, I was doing the press at the time. I’ve heard his comments and I very much believe his comments.
“Sometimes it’s an emotional game and even from myself when you’ve been at the bad end of a 5-1 defeat you’re obviously not too happy and you can be angry yourself, and possibly my reaction is a little bit different if our result was better.
“I do believe what he said that it wasn’t something he’d done intentionally. You don’t want to take the emotions out of the game.”
England manager Gareth Southgate has claimed that the country needs to boot racism out of its own football before criticising World Cup hosts Russia.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.