Speaking after Saturday night's 32-0 loss, Gutherson also declared he would have no issue with the Dragons pursuing Trai Fuller as a potential new No.1 for the rest of the year.
Saturday's defeat left the Dragons with their worst-ever start to a season following a winless opening five rounds, while their nine straight losses is also a club record low.
The Dragons were competitive in the opening four games of the season, but Saturday night was by far their worst performance.
Players were booed at both halftime and fulltime by the Kogarah crowd, prompting co-captain Damien Cook and Flanagan to apologise.
Flanagan had admitted on Friday he needed wins to keep his job, despite believing club bosses had been "rock solid" in their support of him.
The coach then cut a dejected figure in the post-match press conference, vowing not to give up as he admitted the performance was "not acceptable".
The Dragons are not expected to pull the trigger on Flanagan immediately, but there is little doubt he needs to turn things around.
Assistant Dean Young looms as the likely option to take over if Flanagan does not survive the slump, having served an apprenticeship as Dragons caretaker in 2020.
But regardless, co-captain Gutherson insisted the fault lay with the players and not Flanagan ahead of Friday's crunch clash with Manly.
"We're letting him down," Gutherson told AAP.
"He does tireless work, Shane. He leaves no stone unturned. Him and (assistant) Mick (Ennis) and Deano. We're just not doing it.
"We had every chance to do it in the first four weeks and we didn't.
"And then (Saturday night) we just didn't get a chance to play the footy we wanted to, and you can't do that in the NRL."
Gutherson limped from the field at fulltime on Saturday night after pulling up sore in the last set, but hoped it was only hamstring tightness.
If he was to miss the Manly match, the Dragons could have backline headaches, with winger David Fale facing a one-match ban after his boot hit Murray Taulagi's neck while catching a bomb.
That is the least of the Dragons' worries.
Their attack was horrible with Lyhkan King-Togia and Dan Atkinson in the halves, as were their last-play options.
They then surrendered meekly in defence, with Flanagan admitting he had to come up with answers and changes early this week.
"It's embarrassing," Gutherson said.
"We train so hard, we are such a proud club and we want to go out there and do the fans proud and we're not doing it.
"We know how proud the fans are and they have a right to be angry. We're not shying away from that."
Saturday night's loss was followed by a News Corp report that the Dragons were attempting to sign Fuller from the Dolphins for the rest of the year.
The 28-year-old has impressed whenever given a chance at fullback, but has played just nine minutes for the Dolphins this year while stuck behind Hamiso Tabuai-Fidow.
"The club can obviously do what they like. I have said openly for 15 years I've been playing that I will play anywhere," Gutherson said.
"I know what I can do to help a team and I am happy to play anywhere. If they see me playing somewhere else that's the way it is.
"It's nothing against me, I want to win as much as anyone else. If we can make our team better and there is a player out there, I am all for it."
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