Giants were trailing 6-0 at the time and O’Brien had to depart with an injured shoulder, Australian scrum-half Jack Cogger having already limped off in the ninth minute.
But Watson was irate that England international Sarginson - who he coached at Salford last year - was not dismissed.
“It’s a big one,” he said.
“He’s obviously sent the wrong guy off and left one of the best players on the field who shouldn’t be on the field.
“It’s had massive impact on the outcome of the game.
“We told the fourth official and the other official thast he had to speak to hium as he’s all wired up so why he cant talk to him and tell him it’s the wrong guy…
“We even tried to show him on the video on the sdideline that it’s the wrong guy. Why he can’t just speak to him and tell him so he can change the man sent off is lo and behold for me.
“I had the discussion on the sideline with CHrids KEndall for about five minutes. He’;ll be held responsible. Well you’d think he would be We generally all are.
“It’s a huge, huge error. You can see when Greeny’s coming off he didn’t have a clue why.
“Adam O’Brien scores all day long but Sarge just rips his head off. It’s as simple as that.
“It’s a ban and I’d be surprised if he didn’t get a load of games for that but it doesn’t help us.”
Watson conceded his side were not good enough and he praised Salford, saying they “wanted it more” than his side in the latter stages and “deserved” the win,which was only their second this term.
It was Huddersfield’s sixth Super League loss but came after they had seven players report positive Covid tests last week, forcing their game against Wigan Warriors to be postponed.
There has been knock-on effects friom that with the number of players needing to self-isolate and - with fresh injuries - Watson aired his concerns about being able to field a side next Friday when they head to Hull FC.
England play the Combined Nations All Stars on the same night and Giants could see Jermaine McGillvary and Jake Wardle feature for England.
The All Stars squad has not been announced yet but Watson revealed: “We sent an email this morning as we’ve been told we’re having a minimum of five players called up for this international game.
“I’m all for players being international but that can’t be at the detriment of your team.
“And then you hear that Hull (with no England representatives) are only having two players in (All Stars) and they’re sat there near the top of the league.
“They have players like Josh Reynolds, Manu Ma’u, Mahe Fonua, Chris Satae yet we’re not near the top end of the table yet so why would our players be considered for internationals at this moment in time?
“We said if we got one injury today and you took them (Giants for All Stars), we can’t field a team.
“I get the international team and we want a successful England at the World Cup but then you hear (St Helens hooker) James Roby doesn’t need that intensity of game apparently.
“But that was the whole reason for this game wasn’t it? To get the best players who will play in the World Cup playing together.”
He continued: “We had two players come back from self-isolation - Aidan Sezer who’d not trained with us all week and Owen Trout - and they did really well.
“But the risk is putting them out there. It becomes a welfare issue. We have one player who’s come back in (after Covid) and he’s eight kilos down.
“He looked like a different person when he walked in the other day.
“If the other boys come in like that, it becomes a welfare issue putting them out there next week.”