In a seesawing 32-30 shootout where defence failed both teams in patches, the Cowboys were sunk by a 76th-minute penalty goal after Mitch Moses was hit high.
After Moses ran the ball on the last, the Eels halfback spilled it while falling after being ankle-tapped by Heilum Luki.
But he challenged the call, with the bunker finding Cowboy Tom Chester had collected Moses in the head with the Eels halfback just inches above the ground.
"It's not the reason we lost the game, it was our own fault," Cowboys coach Todd Payten said.
"I would hate a big game to be decided by that call. He had dropped the ball, the play was essentially dead.
"For the bunker to intervene like that, it's hard to cop ... Mitch was on the ground.
"But we had several chances to ice the game, so you get what you deserve."
Cowboys captain Reuben Cotter also argued it should not have been a penalty.
"I feel like common sense has to prevail with calls like that," he said. "It's not the reason we lost the game, but he was making a play for the ball."
Moses was far more direct, adamant it was the right call.
"If you get hit in the head, you get hit in the head. That's what the penalty is," Moses said.
"Obviously I am very low and I understand, but I got hit in the head, so I am just playing to the rules."
The result means Canterbury are still alive in the race for the finals, albeit two points behind the Cowboys and with North Queensland having a bye next week.
Manly, Melbourne and Canberra also remain in the hunt, but would need to win their last three and have the Cowboys drop their final two games at home against Wests Tigers and Canberra.
The late penalty aside, the Cowboys are well aware defence remains a bigger issue ahead of the finals.
North Queensland have all the attacking guns to fire come finals, with Jaxon Purdue starring at half with a long cut-out ball for one try and a stepping run for another.
Reed Mahoney was dominant at hooker, while the Cowboys scored one of the tries of the year to lock up the scores at 24-24 when the ball went from right to left and back to the right through five passes and two kicks before Chester crossed.
But their leaky night also came just a fortnight after conceding 82 points to the Roosters, with North Queensland's defensive record the worst of any top-eight team.
The tone was set when Parramatta winger Brian Kelly went 60 metres from the opening kick-off, while the Cowboys also conceded six first-half penalties.
Not to be outdone by the Cowboys' ball-playing, Parramatta also had plenty of attacking flair.
It was big prop Junior Paulo who responded to level the scores at 30-30, with a lofted 35-metre cut-out ball in the lead-up to a Jordan Samrani try.
Moses also had three try assists and broke through the line in the lead-up to a Tallyn Da Silva penalty try.
And his off-contract halves partner Ronald Volkman again pushed his case for another deal, scoring one try and putting a grubber-kick in for a Josh Addo-Carr four-pointer.
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