San Francisco coach Steve Mariucci suspended Owens for one game and fined him a week's salary, worth $24,294, for sprinting to midfield and celebrating on the Cowboys star logo. Owens, the 49ers' leading receiver, will not practice or be in team meetings this week.
"This decision is based on how we intend to conduct ourselves," Mariucci said. "It disturbs me when the integrity of the game is compromised in any way, shape or form."
Mariucci called Jones on Monday to apologize. So did 49ers vice president John York and vice president-general manager Bill Walsh.
"They all told me how much they regretted the taunting," Jones said. "They were all very disappointed with what happened, and genuinely regretful. As an organization, they showed a lot of class. I appreciated that."
Owens' first celebration sparked a chain reaction. Cowboys running back Emmitt Smith ran to midfield after he scored, slammed the ball on the field and stared at the 49ers bench. When Owens celebrated the second time, he was knocked down at midfield by Dallas safety George Teague.
Teague, who was ejected, will be fined an undisclosed amount and could be fined along with safety Darren Woodson for skipping the team's postgame meeting, coach Dave Campo said.
"I don't think taunting has any place in the game at all," Campo said. "There's no room for that in the game. Both teams should be ashamed of themselves. I think frustration sometimes gets into that. That's something I have to guard against and make sure that we have our team understand that's not the right way to handle the situation."