Hibs were seventh when Butcher left Inverness Caledonian Thistle to take over at Easter Road, but just six wins in his 28 matches at the helm resulted in his side being relegated from the Scottish Premiership.
Their fate was confirmed this afternoon as they blew a two-goal first-leg lead against Hamilton Academicals before going on to lose the playoff final on penalties.
"You don't know how I'm feeling. 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. You just can't halt the slide and you can't halt the losses," Butcher told reporters.
"Even today we've had opportunities to see the game out. Seventy-five seconds left and we're 1-0 down, and I'm thinking, 'okay, we'll take a 1-0 defeat, that means we stay up'. But we can't even do that.
"And then the penalties become a lottery. We miss the first penalty too. We are where we are, and it's not because of this game, it's because of what we haven't done over the whole piece, really."
Despite speculation to the contrary, Butcher has insisted that he wants to remain in charge of the club next season.