Bruce saw Southampton amass a 3-0 lead after just 37 minutes at St Mary's, courtesy of goals from Morgan Schneiderlin, Rickie Lambert and Adam Lallana.
While Yannick Sagbo pulled one back 10 minutes after the break, Steven Davis capped off a comfortable victory late on for the hosts, who moved up to third in the Premier League with their victory.
While Hull dropped to 12th, they remain the highest placed team of those that were promoted from the Championship last term, and Bruce was far from despondent after the defeat.
"Sometimes you have to hold your hands up. We've been beaten by a very, very good side here today," he said.
"We couldn't come to terms with them in the first half. The better team won by a million miles.
"We've just been promoted, and our aim is simply to stay in this league. The longer we stay here, the better we'll become."
Next up for Bruce's side is a potentially crucial home clash against fellow promoted outfit Crystal Palace, before they face difficult meetings with title challengers Arsenal and Liverpool.
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