Harbaugh said Monday that Matthews threw one punch and slapped 49ers left tackle Joe Staley when they tussled following Matthews' late hit on quarterback Colin Kaepernick in the second quarter of San Francisco's 34-28 season-opening win against Green Bay on Sunday.
"If you're going to go to the face, come with some knuckles, not an open slap," Harbaugh said. "I think if that young man works very hard on being a tough guy, he'll have some repairing to do to his image after the slap."
Matthews promised leading up to the game that Green Bay would target Kaepernick after he ran for a quarterback-record 181 yards to beat the Packers in the playoffs eight months ago, and Matthews did just that. On the play, he threw his right arm around the lower part of Kaepernick's neck.
"Like I said last week, usually a man will tell you his bad intentions if you just listen. That certainly was a cheap shot, launching, clotheslining to the neck-head area," Harbaugh said. "Bad play."
Packers coach Mike McCarthy called it a "bad decision" by his four-time Pro Bowler.
"I think he was overzealous," McCarthy continued. "I know he left his feet and, you know, playing hard. I think it's football. I think much is blown out of proportion. Clay played very well in the game. That was probably one of his couple of bad plays."
Defensive coordinator Dom Capers disagreed with Harbaugh's contention of Matthews being a dirty player.
"I don't believe that," Capers said. "I think Clay is an aggressive player that's going to play with a lot of emotion. I thought he played a good football game yesterday. You saw him come and make minus-yardage plays. You saw him sack the quarterback. It was unfortunate that the sideline play, I think he just misjudged where he was really. We have to make sure that doesn't happen, but I like the aggressiveness Clay plays with. He plays with his heart and a lot of emotion. I've been here with Clay now – this is five years and I certainly don't believe that."
While Matthews was flagged for a late hit, Staley received an unsportsmanlike conduct penalty that Harbaugh didn't think was right.
Staley immediately came to Kaepernick's defense on the play. The penalties were offset and the 49ers scored on the next play, which officials later said should have been fourth down rather than a repeated third down.
The NFL said Monday that a review showed Staley should not have been penalized.
"After reviewing the play, Vice President of Officiating Dean Blandino determined that Joe Staley should not have been penalized," spokesman Randall Liu said in an email. "It should have been first-and-goal for the 49ers from the Green Bay 3-yard line."
"That's what I saw," Harbaugh said.
Harbaugh praised referee Bill Leavy and his crew, and said San Francisco would have gone for it on fourth down anyway.
"First of all, it never should have been offsetting penalties, in my opinion," Harbaugh said. "All in all, there's a lot of things going on in that stretch. The other one was the entire Packers bench cleared, practice squad players, coaches. Members of the Green Bay Packers are all out of their bench area down along the goal line. There was no repercussion for that as well."
While Staley said after the game he needs to control his emotions, he insists he will defend his quarterback in a case like that.
Harbaugh said it's rather simple when coaching a situation like that.
"When guys are going at each other after the whistle, and looking to push and shove people, just lock up, protect yourself," he said. "Not going to back down from it, we're not going to get pushed all around after the whistle when it's not being called, when the first offense is not being called. You have to have a plan. For us, it's not to go pushing and throwing punches, it's to lock up and protect yourself. And Joe did that about as well as you could do it. If you call somebody for that then you're going to have 30 flags, 30 times. That's happening all the time in our league after the whistle."