The Tigers, who lost 1-0 in the Premier League on Sunday, were beaten 8-7 on penalties after their Capital One Cup fourth-round tie finished 2-2 after extra time.
"I've not really had much luck here in the last couple of days," the Hull manager said.
"But the team showed their resilience and what they're about. I thought we were going to do it when we scored in extra-time, but it was not to be."
Bruce's misery was compounded by the news that he has been charged by the Football Association for his post-match criticism of referee Michael Oliver, who awarded Spurs an 80th-minute spot-kick for a handball by Ahmed Elmohamady.
Bruce said on Sunday after the penalty call: "It was a joke decision.
"I have to ask the question, would we have got it? In my opinion, he (Oliver) couldn't wait to give it."
"I've been charged," Bruce said. "Mike Riley rang me on Monday morning telling me they've made a huge mistake.
"What am I supposed to say? "I thought the referee here was tremendous.
"We like to see what we've witnessed and let's not lose that. What is the law and what is it supposed to be? I'll argue my case.
"It will cost me a few quid, but I'll do it."
Bruce claims Hull games are not officiated by the most high-profile referees.
"We don't get the big referees. Are we not as important as the big clubs?" he said.
"Although I suppose Michael Oliver is supposed to be one of the top referees but I can't seem to remember Howard Webb coming to Hull very often.
"We've had a bad decision and a bad couple of days but we'll see what the FA say."
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- Premier League