The Tigers could have consolidated their position in the automatic promotion places of the npower Championship and went ahead through George Boyd.
But second-half goals from Darius Henderson and Lewis McGugan ensured Forest made it six wins on the bounce.
"We've done enough to win two matches, that's the biggest disappointment," Bruce 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."