Darren Moore’s side were toothless as the Bluebirds romped to victory, putting Huddersfield to the sword with relative ease.
It was a result that quickly brought the Terriers back down to earth with a bump, following their victory over Queens Park Rangers at the weekend.
Nagle took to social media to address fans following the defeat, blasting the display as “unacceptable”.
Posting on X, he said: “An unacceptable performance. Our supporters deserve so much more.
“We have to do better, from the boardroom to the pitch, and it starts with me. You want to vent to someone? Can’t blame you.
“So vent to me, I can take it. We WILL do better, this I promise. KN.”
Huddersfield currently occupy 19th place in the Championship table, sitting six points above the relegation zone.