Hibees youth player David Paul, 18, passed away at his home in the early hours before 13-year-old Jamie Skinner, who left the Jambos academy two weeks ago, died after collapsing on the pitch playing for Tynecastle Boys club under-14 side.
Butcher revealed the Easter Road club were in a state of "disbelief" while Locke spoke of the devastation felt in the maroon half of the city after the events.
"You can sense the shock at the training ground today," said Butcher.
"Every single member of the squad, the club, everyone at Easter Road and the training centre, are absolutely devastated.
"It is an utter tragedy, mainly for his family of course but also for his good friends and the football club.
"Everyone is still trying to come to terms with it. You can't understand why it happens, it is beyond everyone's comprehension.
"He had been at Hibs since he was 10 years old, he was in the second year as a full-time player and he was much loved by everyone.
"He was a quite unassuming boy who got on with his job, a great professional, a great member of the squad.
"I have three hulking boys, bigger than me, and I just don't know what would happen if I lost one of them so our thoughts are with his family. It is terrible news for them.
"Both clubs in Edinburgh are mourning the loss of good characters as well as good players, it really puts it into perspective.
"All we do is play a game of football. Period. The things that really matter in life is family and life itself."
Speaking at his pre-match press conference ahead of the game against Kilmarnock on Boxing Day, Locke said: "It is tragic. We are all devastated. It puts things into perspective.
"We think we are having difficult times but for us and Hibs, to lose two young players the way we have done is tragic.
"My thoughts go out to both players' families because it must be absolutely horrific for them.
"He (Jamie Skinner) turned up yesterday expecting to play football and he has lost his life so deepest sympathies for both families and everyone at the football club is hurting.
"We just hope both families can get over it at some point."