The person spoke on condition of anonymity because the punishment had not been made public. The exact size of the fine was not known and it was uncertain whether the punishment would impact Dockett's participation Sunday in Seattle.
Dockett refused to go along with a coach's directive to allow the Jets to score late in the game so the Cardinals could get the ball back and go for the tying touchdown.
He indicated in a tweet Friday night that he was appealing through the players' union.
"Thank God for the (at)nflpa," Dockett wrote, "that's all I got to say... I ain't got no worries."
The fine first was reported by XTRA-AM 910 sports talk show host and Cardinals reporter Mike Jurecki.
The punishment stems from a directive from the coaching staff to allow the Jets to score when they had the ball deep in Arizona territory in the final minutes. Dockett refused and got into a heated on-field argument with safety Kerry Rhodes about it.
The issue became moot when the Jets' Shonn Greene purposely downed the ball at the Arizona 1 and ran out the clock.
Defensive coordinator Ray Horton told reporters Friday that he was the one who suggested to coach Ken Whisenhunt that the Jets be allowed to score. Whisenhunt has declined to discuss the situation, calling it an internal matter.
The emotional confrontation between Dockett and Rhodes came as the team headed toward its eighth consecutive loss. The prospects that the team would score in the final seconds with no timeouts were obviously dim, because it was one of the Cardinals' worst offensive performances in franchise history. With Ryan Lindley making his second start, the Cardinals tied a franchise low with five first downs and were 0 for 15 on third-down conversions.
Whisenhunt refused to replace Lindley with John Skelton, who was benched three games earlier. But Skelton will return as starter against the Seahawks.
Dockett said earlier this week he had apologized to Rhodes and the two had agreed to move on. But Dockett emphatically said he had never quit in a game and never would.
"It's something that I don't believe in, something that I didn't understand," Dockett said then. "It was frustrating at the time. At the end of the day, I am never, never going to lay down and quit. I've been playing football for over 20 years. I've given this organization, I've given Florida State, I've given my high school everything I've got. I love the game. I play with passion and I'll never quit."
The emotional, 6-foot-4, 290-pound, 31-year-old lineman is in his ninth NFL season, all with Arizona. He made the Pro Bowl in 2007 and 2009.
He earns $3.4 million this year on a contract that runs through 2015.
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