Tyrone manager Mickey Harte says Seán Cavanagh’s sending off during Saturday's match contributed to the lack of composure in the final moments of the match.
The Red Hands were defeated 13 points to 12 by Mayo.
Mayo manager Stephen Rochford meanwhile, admitted he was nervous as his side sought to close out a tight game by holding possession.
Tyrone were unable to convert the opportunities they were given, and the Connacht men held out to win by a single point.
They now book their place in a sixth successive All-Ireland semi-final.