Asmir Begovic saved a Tom Huddlestone shot and Liam Rosenior headed over as Hull could not find the breakthrough in the first period, while the Stoke keeper then made a fantastic save after the break to deny David Meyler's deflected shot.
The Tigers were made to pay when Peter Odemwingie struck in the 62nd minute, firing in from the edge of the box after collecting the ball from a stray Ahmed Elmohamady pass.
The defeat came after a 2-1 reverse at West Ham in midweek and Bruce rued poor goals in both games.
He told Sky Sports: "I've been in it long enough in this league we play in and if you make mistakes like we've done twice in two games - an own goal against West Ham and a horrible pass from Elmohamady today - I mean Odemwingie's done well after that but it's ridiculous really the opportunity we've gifted them.
"From being so comfortable in the game away from home - I can't remember being away from home and being so comfortable - but we've missed a couple of glorious opportunities.
"Good chances we've missed and we've gifted them the goal which unfortunately is one of them disappointing afternoons."
The defeat means Bruce's side have now lost four out of their last five league games to remain on 33 points with seven matches to go.
He added: "There was a lot of tired bodies towards the end. We did terrifically well to play for an hour with ten men (against West Ham) on Wednesday and I think that showed towards the end when we were chasing it.
"But we should never have been in that position to chase it - we've gifted them the goal which obviously is disappointing for us because all season we've been fantastically disciplined to not give much away, if you look at our goals against.
"And unfortunately we've conceded two in a week where we have to hold our hands up and say we've made blatant mistakes."