Hinkley will lead the Power for a 13th and final season before passing the baton to senior assistant Carr, who has signed a three-year deal from 2026 onwards.
The succession plan was confirmed by the club on Wednesday.
It prompted immediate criticism from Carr's 2004 premiership teammate Kane Cornes, who claimed the move had ended the Power's 2025 flag bid before the campaign had even started.
"It automatically rules out Port Adelaide for any shot of the premiership this year," Cornes said in a video posted on social media.
"(You're) clearly not changing coach before the start of the season if you think you're going to win the premiership.
"So don't even consider, Port Adelaide fans, that they are a chance this year."
Hinkley said he "gets on well" with Cornes but fired back at the 300-game former midfielder's criticism.
"There's no accountability to opinions," Hinkley said.
"I'd love to have some accountability to opinions, like I (have) and what Josh (Carr) does and David (Koch) does every week.
"Have some accountability to what you say."
Port chairman Koch laughed off Cornes' comments.
"At this time every year usually the commentators - Kane and the mob - come out and say the biggest slider is going to be Port Adelaide or the window is closing," Koch said.
Koch defended the decision to go public with the coaching succession plan, rather than waiting until the end of the season.
He said it would remove the distraction of speculation around Hinkley's future, which has hung over the club in recent years.
"Good clubs transition smoothly and our No.1 priority is to have no disruption and no distraction to the football program," Koch said.
"Stability, I think, is a key ingredient into a successful sporting organisation."
Cornes also backed Carr's ability to step up as a senior coach but queried the club's decision not to explore other options - such as John Longmire, Adam Simpson, Nathan Buckley and even current Geelong coach Chris Scott.
Koch defended that call, saying the club wanted a first-time senior coach and had a strong track record of developing coaches and leaders from within its own walls.
Hinkley holds the unwanted record for most AFL games in charge without reaching a grand final - 274.
The 58-year-old has led the Power to four losing preliminary finals and has faced concerted criticism from a section of the supporter base who don't think he can take them to a premiership.
But Cornes said Hinkley deserved to be celebrated for his ability to put Port in contention, having made seven finals appearances since taking over in 2013.
"I hope this gives an opportunity for everyone to appreciate the coach than Ken has been," Cornes said.
"I know this will satisfy many disgruntled Port Adelaide fans and now they can look to the future beyond Ken Hinkley.
"But I think we've at least got to acknowledge the unbelievable coach that he has been, and (he's) had Port Adelaide in contention for most of the years.
"He hasn't got where he wanted to go and where Port Adelaide fans wanted him to go, but every year you rock up and know Port Adelaide were going to have a crack."
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