The 31-year-old continued the Crucible curse of no first-time winner defending their title as he crashed out with a 13-9 defeat.
Selby has admitted that his Scottish opponent - playing in the tournament for the first time - was a worthy victor and has tipped him to go far in Sheffield.
He told reporters: "He played fantastically all match and thoroughly deserved to win. I played really poorly in the second session.
"Every time he got a chance he seemed to punish me. I said to him at the end that if he played like that there's no reason he can't win it.
"I've known Anthony for a few years now. I've no embarrassment in losing. You look at the greats who've won it for the first time and not defended it."
Leicester-born Selby beat this year's favourite Ronnie O'Sullivan in the 2014 final.