Cook was a shock axing from the Rabbitohs' side to face Cronulla on Saturday, with Demetriou fighting to save his job.
A NSW State of Origin hooker last year, Cook said on Wednesday he did not feel as if he had become a scapegoat for Souths' woeful 1-4 start to the NRL season.
And, while his emotions weren't directed at Demetriou, he was disappointed to be dropped for the first time since becoming Souths' first-choice hooker in late 2016.
Damien Cook was shocked to be dropped. (James Gourley/AAP PHOTOS)
"Of course I'm angry," Cook said on the Big Sports Breakfast on Wednesday.
"(I'm) frustrated, angry and sad. I had all the emotions yesterday.
"Because I do want to be out there on the field giving my best for the team to get us out of where we are.
"No doubt yesterday shocked me. It was quite a tough day.
"But I can't sit there and mope around. I trained really well yesterday and gave the team some good opposition to train against."
The 32-year-old was adamant his absence would be brief, and that he could fight back into the NRL side quickly after Peter Mamouzelos' selection at No.9.
"It's been tough. Obviously changes needed to be made and he needs me to be better," Cook said.
"The leaders of the team need to lead the way and we mustn't be doing a good enough job with that.
"I know I have more to give. I felt like I was building into this season, and I am confident I will be back."
Cook's comments came as former Rabbitohs captain Adam Reynolds threw his support behind Demetriou and embattled pair Latrell Mitchell and Cody Walker.
Mitchell will miss the clash with Cronulla after copping a three-game ban for a forearm to Shaun Johnson's head against the Warriors.
With Lachlan Ilias first dropped and then injured, it leaves Walker as the only remaining member of their round-one spine.
Walker has also been below par this year, as Souths' end-of-season woes from 2023 carried into this season.
Also lingering are claims that Demetriou has afforded preferential treatment to Mitchell and Walker, something Brisbane skipper Reynolds said he had not seen while at Redfern.
"When I was there they were terrific team players and got the job done," Reynolds said.
"I had no problems when I was there with them.
"When you aren't playing your best football, it's easy for outsiders to make judgement on these players.
"But their teammates and ex-teammates would love to have them in the team every day."
Latrell Mitchell tries to get away from former teammate Adam Reynolds during their round-two clash. (Dave Hunt/AAP PHOTOS)
Reynolds played under Demetriou when the coach was Wayne Bennett's assistant at Souths.
"I'm not down there so I don't know (what is going wrong) but I feel for the boys and JD (Demetriou)," Reynolds said.
"I worked with JD before and I know he is a great coach."
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