Spy looks angry at himself, because if you get caught you've failed as a Spy. That blow to his ego and to his professional pride must hurt more than the injuries he sustained during his rough capture and interrogation. Thankfully, Grey Mann is a gloater. That is something Spy can work with. Even without his knife and his disguise kit and invisibility watch, Spy can rely on his talent for manipulation.
Or maybe Spy let himself get captured on purpose, to get close to Gray Mann and his secrets, hoping the man does not know about the mercenaries' source of immortality... the respawn. Dying was always part of the Spy's plan.