The Falcons led 21-0 at the break in the International Series game, but failed to score a point in the second half, and the Lions mounted a comeback as Matt Prater kicked a game-winning field goal as time expired.
Smith told reporters: "When you lose a football game, it hurts. We felt coming into this game that if we took care of what we needed to today that it would put us in a very different situation than what we've been over the last couple of weeks, because of the bye week and two division games coming after the bye week.
"You know, it's a tough way to lose a football game. There's a bunch of guys that feel just as bad or worse than I do."
The Falcons are 2-6 in their season following their defeat to the Lions.