Riyad Mahrez scored the decisive goal for the visitors at the KC Stadium on Sunday, but Hull spurned a host of chances as they searched for an equaliser.
Bruce watched on as Jake Livermore and Abel Hernandez were both denied by the post in the closing stages.
And Bruce admitted he had never seen his side dominate a Premier League game and not win.
"I think we've been in the Premier League for 18 months and I can't remember having so many chances in a game, not at this level," he said.
"But the one thing you have to do is score, we should be scoring, we hit the post and had them cleared off the line three or four times.
"I couldn't fault their effort and endeavour, it was relentless in the second half, but it is just one of them things. You've got to take chances at this level.
"And [then] it turns into one of those awful afternoons where we don't deserve to get beat, and the only shot they've had at our goal they’ve scored from."
Defeat means Hull are one place above the relegation zone, but they are now level on 16 points with the two sides immediately below them, with Leicester just three behind at the bottom of the table.
Bruce knows his side missed a chance to put some daylight between Hull and the bottom three, leaving them firmly in the battle to stay up this season.
He added: "To go nine points ahead of Leicester would have taken a lot of clawing back, so in terms of the magnitude of a win, it would have been huge.
"We've given Leicester a lifeline, and it is all to play for in the second half of the season."
