Sunderland and Norwich City have both been fined £30,000 after the touchline confrontation at Carrow Road.
Both clubs have also been warned about their future conduct after the incident which involved players and coaches from both sides plus Sunderland manager Sam Allardyce.
The incident was sparked after Sunderland full-back DeAndre Yedlin was sent flying into the advertising boards by Norwich captain Gary O’Neil in the opening minutes of the match.
It angered the Sunderland coaching staff who were just metres away from the incident and players from both sides waded in.
Allardyce then appeared to shove Norwich substitute Cameron Jerome out of the way before confronting O’Neil.
Allardyce said he was simply ‘protecting his players’ but both clubs have now been fined.
Sunderland accepted the charge but Norwich City contested the charge.
A statement by the FA read: “Both Norwich City and Sunderland have been fined £30,000 and warned as to their future conduct for failing to ensure their players and/or officials conducted themselves in an orderly fashion.
“It follows an incident which occurred in the fourth minute of their game on 16 April 2016.
“Norwich contested The FA charge in relation to this matter, however, it was found proven following an Independent Regulatory Commission hearing.
“The charge for Sunderland was accepted by the club.”
The Sunderland boss joked about the incident post-match, with opposite number Alex Neil playing the incident down too.
Allardyce said: “I was a bit disappointed the fourth official didn’t stop the Norwich players encroaching into my technical area!
“I was protecting my box and my players at the time. I got a bit carried away, there was a lot of emotion in the game.
“It was such a big game and I don’t know why they came running over as much as they did but I was going to protect my players and mob.
“In the end [referee Andre Marriner} said ‘calm down, will you?’
“I said It would try my best! I didn’t know I still had that strength!”