Several hundred angry fans gathered outside Easter Road and chanted for Butcher and chairman Rod Petrie to go after the dramatic SPFL Premiership play-off final defeat by Hamilton Academical.
Hibs will be in the second tier next season for the first time since 1999, alongside Hearts and Rangers, after Hamilton wiped out the Edinburgh side's 2-0 first leg lead and won 4-3 on penalties. There had been rumours before the match that Butcher was poised to resign for personal reasons. He denied that but admitted he could be sacked after an appalling set of results caused them to slide all the way down the division. They were seventh, and within sight of a top-six place, when he replaced Pat Fenlon in November.
"If it's down to me I will be here," said Butcher when asked about next season. "There was stuff on social media that I would be quitting no matter what the result was. But that was never the case. I want to continue, because I would like the opportunity to be able to restructure the club in the right way. I think that situation is out of my hands now.
"We're due to meet the players and discuss their future. I'll have to speak to the chairman and see where we are on that one. It's heartbreaking. We're numb at the moment and it's a horrible, horrible feeling. It's happened before with Caley Thistle for me as a manager, and we bounced back straight away after that. And if I'm still in charge next year, that will be the aim and ambition of the club.
"In many aspects, the club needs a whole restructure. It needs to be changed round, it needs to be improved, and it needs to be built from stronger foundations. If I'm allowed to we will sit down and look at a way forward. This club has been in the doldrums for quite some time but there are lots of things we can do. There would have been a restructure if we had stayed up. It was going to be a big rebuild, it will be an even more massive one now.
"I'm the manager. I've had plenty of opportunities to stop the slide and to have won games. I haven't done that enough. I accept responsibility because I've had opportunities to make sure that we were safe. It's been like watching a car crash the last two or three months, and you do everything you possibly can to stop it and you just can't."
Hibs were 75 seconds from safety when Tony Andreu scored, adding to Jason Scotland's 13th-minute opener. Goalkeeper Kevin Cuthbert then saved from Kevin Thomson and Jason Cummings in the shoot-out.
Alex Neil, the Hamilton player-manager, was jubilant after seeing off Falkirk and Hibs to be the beneficiaries of the new SPFL play-offs, and heaped praise on his side for taking the club back to the top flight for the first time since 2011. "Over the two legs, we were desperate to win and Hibs were terrified to lose," he said. "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.
"It was unbelievable but I'm more pleased for the players than I am for myself. They've put so much into this season. We've not got a big fanbase like Hibs but this was for our loyal fans."