Cook is one of three St George Illawarra players signed by Castleford next year to play under Carr, who was an interim and assistant coach at the Dragons.
The 38-year-old was initially stood down pending a club investigation earlier this month, before he later exited the Tigers due to "personal reasons".
Dragons winger Tyrell Sloan has already stated Carr's exit has put a "big dent" in his plans to move to England, while Mat Feagai said it had also created uncertainty.
But Cook said his plans won't change, with the former NSW and Kangaroos Test hooker's 14-year NRL career to end in a fortnight after games against Manly and Parramatta.
"I'll be over there," Cook told AAP ahead of Friday's clash with the Sea Eagles.
"I've had the conversations with my wife and my kids and obviously it's a big move for them as well.
"But once I had them on board we've really been focused on that. I'm committed to that.
"This great game has given me a lot, and it's just another thing that's going to give me a chance to go overseas, play footy over there and show the kids the world."
Cook said he had reached out to Carr to check on him, and also made contact with Castleford officials while the Australian had been stood down.
But the 35-year-old said he too was none the wiser on the reasons behind his exit.
"I told them how I felt about him, and obviously I spoke to the owner of the club and the general manager as well.
"I didn't want to get too involved because I didn't want it to take away from just enjoying my time here. There's nothing I can do from over here.
"He's put a lot of effort into that and no doubt he's hurting. He's a very passionate person and obviously a big reason why we went there.
"He's got some good recruits, but I'm not sure exactly what he's got planned. No doubt he'll find something.
"I really loved him as a coach and that's obviously a reason why I was connecting with him over there."
Cook said it had not yet sunk in that the next two games would be his last in the NRL, after a career that has included more than 260 first-grade games and a grand final for South Sydney.
But the fact his future was decided in May had made it easier for him to process the situation, with his last game to come at WIN Stadium where he regularly attended as a child.
"I've really just sort of sat back and just tried to soak it all in," Cook said.
"Every time I go to a ground for the last time as a player, just have a good look around when I run on and just really soak it up."
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