Kane's double after the break secured three points for Spurs on a day in which United had 22 goal attempts but failed to finish where and when it mattered either side of Matt Ritchie's equaliser.
After the 3-1 defeat, Bruce said afterwards: "There's the difference. That quality at the other end of the pitch.
"They are worth their weight in gold.
"We could have done better defensively with the second after we'd just scored.
"Unfortunately sometimes you don't get the result you deserve."
He added: "The way we played I couldn't complain.
"I'm frustrated as we've gave away two more soft goals."