The Dragons were booed by fans at a half-empty Kogarah on fulltime on Saturday, after slipping to the club's worst ever start to a season with a winless opening five rounds.
The result also left the Dragons with the longest losing streak in the joint-venture's history, which now sits at nine and dates back to August.
"It's not good enough for this club," said Flanagan, who cut a devastated figure in the post-match press conference.
"I don't accept it, I am not happy with it, I am terribly disappointed and I am sorry.
"I fully understand the frustration, I am as frustrated as anyone.
"All I know is it hasn't worked this year, but I'm not going to give up."
Making matters worse for the Dragons was co-captain and fullback Clint Gutherson limping up the tunnel on fulltime with a hamstring injury.
On the flip side North Queensland now have three straight wins, just weeks after their coach Todd Payten's job security had appeared as bleak as Flanagan's following a 0-2 start.
Flanagan now needs a revival of that kind from his Dragons, after he conceded to AAP on Friday he was "a realist" and knew he needed wins to remain coach.
In two-and-a-bit seasons at the club he has blooded a number of young forwards, but the Dragons' finals drought is now at risk of reaching an eighth year.
They had at least been in all of their first four losses until late in the game, but were never in the contest on Saturday.
Scott Drinkwater and Jaxon Purdue blitzed them, with Drinkwater kicking a 40-20 before the Cowboys' first, then slicing through the Dragons' left edge two plays later to score.
The Dragons' best attacking raid in the first half ended when Dan Atkinson kicked on the second tackle, which was easily scooped up by Drinkwater.
Moments later it was 10-0 when Jake Clifford offloaded for Purdue to go 65 metres and score, before Clifford later grubber-kicked for Purdue's second on halftime.
Nothing summed up the Dragons' day more than a 90-metre Braidon Burns try, when a wayward Lyhkan King-Togia pass went to ground from a Dragons scrum.
Making matters worse for the Dragons was the fact it came while the Cowboys were down to 12 men, with Reuben Cotter sin-binned for a professional foul.
King-Togia in particular had a poor afternoon in place of the concussed Kyle Flanagan, while Atkinson's kicking game was below par, with multiple grubbers going dead.
"It just wasn't good enough," Flanagan said.
"We looked like we didn't know each other at different stages, passes behind each other, a lack of cohesion. It was very disappointing."
In contrast, Clifford was great at No.6 for the Cowboys, and Purdue had a field day outside him.
The centre finished with 189 metres to go with his two tries, and also sent Taulagi over for one in the second half.
Burns and Sam McIntyre both limped off with ankle injuries in the win, the only sour note for the Cowboys.
"We've got a team, we've just got to keep believing," Payten said.
"We've adjusted to the way the game is being played. We've got some footy in us."
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