Finnegan said he plans to appeal the fine. Johnson was scheduled to be available after a practice Monday evening.
"He snapped. He started throwing blows," Finnegan said of Johnson.
Finnegan set off the brawl by jabbing at Johnson's neck and face mask at the line of scrimmage. Johnson ripped off Finnegan's helmet and landed at least two punches to Finnegan's head and neck. The two spun each other, and Finnegan tore off Johnson's helmet before players and referees intervened.
Johnson apologized after the game.
"I would like to apologize to the organization, our owner, and my teammates," Johnson said. "What happened out there today was not me. I just lost my cool and I wish that I could take back what happened, but I can't. It's over and done with now."
This is the second time they scuffled. Last season, Johnson was fined $7,500 for taking Finnegan to the ground by the face mask.
"I guess he got his money's worth," Finnegan said of Johnson during his weekly radio show Monday night. He also apologized for the way he left the field.
The cornerback said Johnson said some things to him in the fourth quarter, so he decided to "quick jam" the receiver at the line. Finnegan said he thought the play ended once his helmet came off, and if he had punched Johnson, the NFL likely would have suspended him.
"This is the NFL, not the NHL, and it's a higher standard," Finnegan said. "That's the NHL. They fight. They get penalized for that. The NFL, it's not even heard of ... you do that, you're suspended, hands down. That's what I've been taught."
Finnegan's teammate, defensive end Dave Ball, called into the radio show and said he was upset with the NFL's punishment. He called the equal fines with no suspension for Johnson "ridiculous."
"What he's saying is you can criminally assault someone on the football field when they don't have their helmet on," Ball said.
Finnegan was fined for personal fouls in three consecutive games earlier this season and was warned by the league after the third incident to watch his behavior after the whistle.
This was Round 2 between Johnson and Finnegan. Last season, Johnson was fined $7,500 for taking Finnegan to the ground by the face mask during a scuffle after a play in a 34-31 Texans win.
"I have very strong opinions about the fact I think he should not be suspended," Fisher said of Finnegan. "As far as what the league decides to do, that's a league decision.
"It's an unfortunate thing that happens. You've got two very talented, good football players competing, and it's just very unfortunate. It's not good for our game and I'm just disappointed that type of thing happens on the playing field."
The Associated Press contributed to this report.