Bruce insisted all was not lost despite a 2-0 defeat to Tottenham leaving his side on the brink of relegation from the Barclays Premier League.
Second-half goals from Nacer Chadli and Danny Rose mean the Tigers are two points adrift of safety and must win at home to Bruce's old club Manchester United next weekend.
Even victory against Louis van Gaal's side may not be enough, however, with Newcastle and Sunderland currently two and three points ahead respectively.
Sunderland, who also have a game in hand at Arsenal on Wednesday, visit Chelsea on the last day while Newcastle host West Ham.
"It's not lost," Bruce said. "We've got to beat Man United and I haven't done that in 17 years. I've got to turn the tables.
"Maybe there's a twist in it, maybe Man United owe me something after wrecking my knee and my hip and my ankle. We have to try to be positive."
The defeat to Tottenham capped a miserable seven days for Hull, who lost at home to Burnley last weekend before being hit with the news Jake Livermore had tested positive for cocaine.
Livermore, who has been suspended by the Football Association and his club, missed the match at White Hart Lane and could face a ban of up to two years.
"The week has been arguably the worst week I've had in terms of the result last week and then of course the shocking news of what fell on our laps on Wednesday," Bruce said.
"The team and their response today has been magnificent and I couldn't have asked for anything more.
"I couldn't have asked for them to play any better after the woeful performance last week.
"The frustration is how we produced what we produced last week and what we produced today.
"The reason we're in the bottom three is pretty evident today.
"We've had five or six really glorious opportunities and at this level you've got to take them."