The Seagulls lost 4-0 at Anfield in their final game of the Premier League season as Liverpool won with goals from Mo Salah, Dejan Lovren, Dominic Solanke and Andrew Robertson.
The game was live on Sky Sports and at full-time, March was caught on camera putting his middle finger up as he applauded the Albion fans.
March said he was responding to his mates telling him to hurry up as the winger is off to get married.
March tweeted: "I wanted to apologise for gesture I made, It was a silly thing to do. It was aimed at my mates in the crowd as they were telling me to hurry up as I have to make a flight to go to my wedding! Thanks to the fans for the amazing support throughout the season!"