The seven-time Pro Bowler knows the league office will likely come calling with a hefty fine.
"There's no getting around it," Woodson told the team's official site. "You all saw it. I'm sure all the people in the NFL who watch the tape, they'll see it. There's nothing I can do about it now. I can't take it back."
"He said it best, he made a mistake," McCarthy said. "He is one of our captains and a key guy young guys look to. He made a mistake, but we move forward."
The punch occurred following a first-down run by Saints running back Pierre Thomas.
Woodson tried to disengage from David Thomas after the whistle blew before launching an upper cut that appeared to land in the tight end's midsection. He was flagged 15 yards for unnecessary roughness on the play.
"I lost my cool," he said. "The guy was blocking me and holding me and I'm trying to get off him. I just lost my cool. Thatâs all on me."
The Associated Press contributed to this report.