The taunts came from the home fans rather than the 1,777 Forest supporters who had made the journey to the south coast.
Derbyshire said via a statement on the club's official website: "It is ridiculous that a journalist can suggest that I was having a go at our supporters. It was clearly the Southampton fans that were taunting the gaffer."
He added: "Our fans were magnificent at St Mary's - as they have been all season.
"The journalist concerned may think it is okay to write something like that but it is me that has to pick up the pieces.
"I would never criticise my own club's supporters, it is not in my nature.
"I apologise to anyone who has taken offence bit I wasn't being critical of our fans."