The Easter Road outfit lost their Premiership status after a 4-3 penalties defeat to Hamilton Academical, who overturned a 2-0 first leg defeat on Wednesday.
Butcher summoned his players for individual meetings at the club's training ground on Monday to discuss their futures. McPake and Thomson were two of the players that discovered their contracts would not be renewed next season.
McPake accepts Hibs' players must take the lion's share of the blame for the club's relegation to the Championship but is disappointed he did not feature in either leg against Hamilton.
"The manager has told me I'll not be part of his plans," McPake told Sky Sports News.
"The blame lies with the players as we got the club relegated but you cannot look entirely at the players.
"I'm gutted. I love playing for this football club. It was some good and some very bad times as well but I'm more disappointed I never got the chance to help the club stay in the division."
Like McPake, Thomson is a former Hibernian captain, and the 29-year-old admits it will be hard for him to leave a club he holds close to his heart.
"I won't be staying," Thomson said. "I'm obviously disappointed. It's hard. Everyone knows how much I love the club.
"Unfortunately the manager has got a different opinion to a lot of people so I have got to respect that and I will be looking for a new job.
"I'm a Hibs fan and it breaks my heart to see the club be in a situation that they are.
"I wish I could have come on and changed the game. I tried my best to try and get hold of the ball and calm us down a wee bit but I think unfortunately from the first minute to the last we were second best to Hamilton.
"I've tried to put in some good performances. Yesterday was not one of them but I think it's hard to judge somebody on one game of football."
Sky Sports News has also learned that current club-captain Liam Craig has also been told he is free to find another club.
Hibernian also confirmed other players out of contract and on their way out are Ben Williams, Sean Murdoch, Paul Grant, Alan Maybury, Bradley Donaldson, Paul Cairney, Tom Taiwo, David Gold and Dean Horribine.
Loan players Daniel Boateng, Danny Haynes and Duncan Watmore all return to their parent clubs.