Powell clashed with home fans after a game which saw Burnley's Kieran Trippier sent off for deliberate handball just 15 minutes in.
Johnnie Jackson's penalty was saved, but the visitors won the game thanks to a second-half Danny Haynes goal.
Powell said: "There was a lot of industrial language and we know that that happens at games from the fans to me and my players, I responded and there were some choice words but I won't elaborate on it because it is gone now.
"Tensions and emotions run high and I understand that but of course if they feel my language was wrong then I feel it was two-fold. I shook a supporters hand at the end and we move on."
Of the game he said: "It's a real tough place to come and they have been doing very well at home since Sean Dyche came in so we knew it would be a tough game.
"We've come away from a hard-fought game, with some contentious issues, and got the three points which you have got to do in the Championship because it is quite an unforgiving league.
"It was a well-worked goal and when we had to be professional and see the game out I thought we did that and we got the got the clean sheet which was pleasing."