The Waratahs stormed to a 17-0 lead in the first half at Sydney Football Stadium before rolling over after the break to lose 26-24 to one of the two South African teams expected to be axed from the tournament next season.
Despite boasting a roster laden with Wallabies players, the Waratahs have won only two matches and have lost five of their past six games to sit second bottom in the Australasian group.
“Every time the team goes out there, of course I feel the pressure. We all feel the pressure,” Gibson told local media when asked how safe he felt in his job.
"When the team is in the situation it is in, those questions are going to be asked. I’ll cop it. Those decisions are beyond my control."
The Waratahs have been in free fall since Gibson took over from Michael Cheika, who guided the team to their maiden title in 2014 before departing a year later to concentrate on coaching the Wallabies.
Semi-finalists in 2015, the Waratahs missed the playoffs last year and their struggles this season have stunned a number of local pundits who tipped them to win the Australian Conference.
Sections of the home crowd booed the Waratahs and filed out of the stadium before the final siren. Local media continued the jeering on Saturday.
"Horror-Tahs: NSW sink into crisis after embarrassing loss to Kings," a headline in the Sydney Morning Herald's website read.
"ATROCIOUS. The NSW Waratahs have sunk to one of the lowest points in their 22-year history after losing to the lowly Southern Kings," the Daily Telegraph's rugby writer Jamie Pandaram wrote in the Sydney newspaper.
Waratahs captain Michael Hooper was ashen-faced after the defeat, having previewed the match as a chance to get their season back on track.
"It was a pretty embarrassing performance from us there," the Wallabies flanker said.
"Our set-piece is terrible at the moment. It's going to be a really tough weekend."
The Waratahs' loss came hours after the Canberra-based ACT Brumbies suffered an abysmal second half fade-out to crumble 56-21 to the Wellington Hurricanes in Nelson after leading 21-14 at halftime.
No Australian side has beaten a New Zealand team nine weeks into the season.
"Truly, this is an awful time for Australian rugby," wrote Pandaram.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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