Gallen on Tuesday copped a three-game ban by pleading guilty to raking the face of the Gold Coast forward, a week after Sharks prop Ben Ross was suspended for seven matches for striking.
The suspensions - and key injuries to the likes of forward Reece Williams (knee, season) and pivot Brett Seymour (knee, four weeks) - have left a black mark on Cronulla's promising start to the season.
But despite expressing disappointment, Stuart said he would stick by his captain.
"Certainly, I wouldn't take the captaincy off Paul for this, no," Stuart told Sydney radio 2KY.
"I've got a bloke that is very passionate and emotional about the job and there's no way that I would take it off him.
"It's just something he has to learn from.
"I'm disappointed, but disappointed for the players.
"We got off to a good start and now we've got six players sitting on the sideline and two players are there because of their own stupid actions."
Gallen had risked being suspended for four games by challenging the charge at the judiciary.
But after viewing video footage of the incident and consulting their legal team on Tuesday morning, the Sharks decided against a hearing.
Gallen re-opened a nasty wound on the heavily bandaged head of Laffranchi during the incident from Saturday's game at Skilled Park, forcing the Titans forward from the field.
The NSW backrower also came under scrutiny by the match review committee for allegedly grabbing the testicles of Titans utility Josh Graham, but avoided a charge through lack of evidence.
Despite the suspensions, Stuart denied there was a discipline problem at the club.
"I don't think it's a lack of discipline," Stuart said.
"We don't have a discipline problem in the joint.
"It's one thing that I keep complimenting the players on is their professional behaviour and the way they behave themselves.
"(Gallen) is a good fellow and he doesn't need his reputation to be tarnished and rubbed through mud but with that carry on I can understand people. I've got to be fair dinkum.
"Paul's very embarrassed by it all but I will support him.
"It's something we will work through and it's something that will make him, one, a better person, and two, a better captain for it."
On the alleged testicle grab, Stuart was honest in saying: "It disappoints me. I'd love to say `no, I didn't see it and let's move on' but yes, I did see it. I have to support Paul on his comments that he wasn't grabbing for the so-called `wheels'.
"I don't know (what he was doing) and that's something to talk to Paul about again."Like