The Easter Road side were demoted from the top-flight after boss Terry Butcher failed to arrest a disastrous run of form that has seen them win just six games since he took charge in November.
They led Championship runners-up Hamilton 2-0 from the first leg of their play-off final but blew up spectacularly in the Easter Road return as they lost 2-0 on the day and 4-3 on penalties to join city rivals Hearts in the second tier.
It was the latest humiliation for a club that has already suffered a record 9-0 Europa League defeat on aggregate to Malmo as well as four derby defeats to the administration-hit Jambos this term.
And it sparked an angry response from around 500 supporters who gathered outside the ground after the match to call for Butcher and the board to go.
But in a statement posted on the club's website, Petrie refused to walk away, saying: "Let me start by saying that I am sorry for a dismal season on the pitch.
"The season started badly last July against Malmo and has finished even worse with relegation to the Championship. The manager and players know that performances have not been good enough.
""We recognise that change is needed. Some supporters have suggested that I should resign as chairman. I take responsibility for the position that the club finds itself in.
"However, it would be wrong for me to abdicate that responsibility at this time and walk away and it would be wrong for the club . Having already announced a few weeks ago that I am handing over my executive responsibilities, it is in the best interests of the club for me to complete that transition to our new chief executive and to oversee the other far reaching changes at the club as non-executive chairman.
"Leeann Dempster has already been appointed as chief executive to lead the club forward. Leeann achieved success at Motherwell and will work closely with Terry Butcher as the club begins the task of assembling a competitive squad for next season. Leeann's arrival is the first of a number of planned changes in the coming weeks and months ahead at Hibernian."
Butcher had already insisted he will not quit before Petrie's statement was posted online.
Internet rumours before the game had suggested he was ready to walk away from the Leith club, no matter what the result. But the former Inverness manager says he is determined to help rebuild the shattered club.
"If it's down to me I will be here," said Butcher. "There was stuff on social media that I would be quitting no matter what the result was. But I don't know where that came from. I want to continue. I would like the opportunity to be able to restructure the club in the right way."
Jason Cummings' double at New Douglas Park on Wednesday had put the Edinburgh men on the verge of safety.
But when Jason Scotland fired home after 12 minutes, the fear in the home ranks was palpable.
They held out until the third minute of stoppage time but came undone when Tony Andreu slammed home a dramatic and deserved leveller.
With no more goals in extra-time, the match went to penalties but Hibs blinked first when Kevin Thomson saw his opening effort saved by Accies keeper Kevin Cuthbert.
And Hamilton's number one put the seal on their promotion party when he blocked Cumming's tired attempt.
Hibs were seventh when Butcher quit as Caley Thistle boss to replace Pat Fenlon but has now taken them back to the Championship after 15 years in the top division.
"It's been like watching a car crash the last two or three months," said Butcher before accepting responsibility for the club's incredible slump. "I'm the manager. I've had plenty of opportunities to stop the slide and to have won football games - that's my job. I haven't done that enough."
While Butcher was in despair, his Accies counterpart Alex Neil was left to celebrate a successful end to his first full year as Hamilton's player-manager.
He said: "I am delighted, for the players and the fans. A lot of people wrote us off but I didn't feel it was a 2-0 game and we played well first half. I told them to believe in themselves and to believe they could do it and once we got the first goal it changed a lot.
"Over the two legs, we were desperate to win and Hibs were terrified to lose. You can understand that, being the Premiership side because I've been there myself when Hamilton went down. But I thought that was the difference between the two teams over the two legs. I even thought we were the better side in the first game, even though we lost 2-0. We were determined to win the game while they looked terrified to lose."
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- Terry Butcher