Hull are hovering perilously just above the Premier League relegation zone after picking up only two points from their last five matches ahead of their trip to St Mary's Stadium.
Any hopes of a Hull fightback at the Liberty Stadium last weekend were effectively ended when David Meyler was sent off for a lunge on Kyle Naughton just three minutes after Paul McShane had given Bruce's men a lifeline.
Bafetimbi Gomis' second goal of the game sealed a 3-1 win for the Welsh side and kept the alarming bells ringing at Hull, who face a difficult run-in with Liverpool, Arsenal, Tottenham and Manchester United among their opponents in the last seven games.
They must first attempt to deny Southampton a third consecutive home win and Bruce knows his side can ill afford another setback on the south coast, as they sit just two points above the drop zone.
"We have to be better at Southampton. To get a result in the Premier League, you usually have to play well," Bruce is quoted as saying in the Hull Daily Mail.
"Sometimes it happens when you have an off day and you don't produce a result. But we can't afford any more now.
"The previous seven games tell me it was a one-off, especially the way we played against Chelsea [in a 3-2 defeat]. We set high standards and need to get back to them."
Fellow strugglers Leicester City, QPR and Sunderland all secured victories last weekend, while Burnley claimed a point against Tottenham at Turf Moor.
Aston Villa and QPR drew 3-3 on Tuesday, but Bruce stressed that Hull must look after themselves if they are to get out of trouble.
He added: "I've always said it but we can't be relying on other teams and other results now.
"You obviously want them to be kind. If we get beaten, you want your rivals to get beaten as well.
"But in realistic terms, the teams below us will keep on picking up points.
"That's why it's up to us to go out there and find a couple of wins and a couple of draws in these last seven games. I'm convinced we can do that and stay up."
Southampton have won their last five games against Hull and could do with extending that run in their quest to secure a place in Europe after losing 1-0 at Everton last weekend.
Ronald Koeman will be hoping Steven Davis (groin) is available to return after missing the trip to Goodison Park, while Shane Long is set to lead the line against his former club.
Hull midfielder Meyler serves the first game of a three-match ban, but Tom Huddlestone is available to return after serving a two-game suspension.
Gaston Ramirez is ineligible to face his parent club, but Bruce could have Curtis Davies (thigh) and Andrew Robertson (knock) back in contention.
