Klopp has since said sorry and reiterated that his snub was not intentional, and Hughton has attempted to end the matter by praising the German for his gesture.
The 58-year-old told reporters: "Credit to Jurgen because he came looking for me afterwards as I was doing the press at the time and I've heard his comments, and I very much believe his comments.
"Sometimes it's an emotional game and even from myself, when you have been on the bad end of a 5-1 defeat, you're obviously not too happy and can be angry yourself and possibly, my reaction is a little bit different if our result is a little bit better.
"Occasionally some of these things happen and I do believe that it was something that he did not do intentionally. You certainly don't want to take the emotions out of the game."
Brighton are next in action when they travel to the John Smith's Stadium on Saturday afternoon to face Huddersfield Town.