The Tigers still sit second in the Championship behind Cardiff, but if Crystal Palace beat Brighton on Sunday, they will be back in the play-off places.
Bruce felt his side should have had at least a point and he had his head in his hands as Robbie Brady hit the inside of the post with a free-kick two minutes from time, with Jay Simpson's follow-up cleared off the line.
"We've done enough to win two matches, that's the biggest disappointment," the deflated Hull boss said.
"I couldn't fault the way we played or the way we've gone about it.
"To be fair to Forest, they've gone for it and played three up front, but the attempts we've had off the line and the post - it's just one of those horrible ones where the luck goes against you.
"Unfortunately it wasn't our day."