Archer, 22, saw his potential winner at Brighton chalked off after a five-minute VAR check adjudged Adam Armstrong to be in an offside position.
Armstrong, 27, made a run towards Brighton's Verbruggen, however, the ball went behind him and into the path of Archer, who fired past a static goalkeeper.
The officials ruled that Armstrong had impacted Verbruggen's ability to stop Archer's shot, something Russell Martin, Tyler Diblng and Joe Lumley all voiced their frustrations about.
Russell Martin off to ask the referee for an explanation after that terrible VAR call. A lot of annoyed voices and you can’t blame them. Two more crucial points lost due to bad decisions. Another apology pending. #SaintsFC
— George Rees-Julian (@rees_julian) November 29, 2024
Former Brighton midfielder Sidwell saw things differently and expressed his view that Armstrong impeded the Seagulls shot-stopper.
He told Sky Sports: "If you are a Southampton fan, staff member or player you would be very disappointed. I get what they are saying with Armstrong making a run.
"His motion, the ball is behind him and he's trying to backheel it. If he gets an impact on the ball, it will impact Verbruggen and where he goes.
Steve Sidwell backed the decision to rule out Cameron Archer's goalSteve Sidwell backed the decision to rule out Cameron Archer's goal (Image: PA)
"Verbruggen is actually waiting for some kind of connection from Armstrong. He's watching the ball exactly as it goes by.
"It does impact Verbruggen's decision-making until the very end where the ball goes in the back of the net.
"Southampton's first form of defence is to attack and that's what has put Brighton on the back foot. They couldn't really recover from that."
Izzy Christiansen added: "It's an incredibly bitter pill to swallow for Southampton. I do feel for them because this epitomises the way they got back into the game.
"There seemed to be a real hunger and energy about the way they played. We are taking fine, fine margins."