Barrow produced everything that should be expected of plucky underdogs enjoying the limelight of their visit to Premer League opposition but the amount of possession Middlesbrough had in their attacking third of the field meant they should have been out of sight before half time.
But even though Afonso Alves scored either side of the interval, Jason Walker's goal 10 minutes from time sparked panic around the Riverside. What is worse for Southgate, whose team had failed to score in their previous three games and are winless in eight Premier League matches, is that, as well as continued speculation linking his best player Stewart Downing with Tottenham, he also lost Jeremie Aliadiere to injury.
Southgate said: "We're in a transfer window that is everything that's wrong about the game but this is what's so good about the game. We had enough chances to win six or seven but it could have been 2-2.
"We hit the post and their keeper made saves and you're sitting there thinking there's a punch-line coming and it did because we didn't do our jobs. We conceded and made life difficult for ourselves for the last 10 minutes and we should have been out of sight by then. We're not ruthless in either box at the moment."
Downing dominated the opening period but the hosts toiled before they finally made the breakthrough midway through the first half when the England winger split the Barrow defence with a pass that was collected by Alves, who had time to check he was onside before prodding past goalkeeper Alan Martin.
Southgate's team continued to create chance after chance but Martin, who is on loan from Leeds, was impressive even though he did not always have to be. After Aliadiere had been stretchered off, Barrow defender Mike Pearson, who was later carried off after being caught by Marvin Emnes, had a drive deflected on to the post by Josh Walker.
After the restart, Brazilian forward Alves, who has frustrated since he arrived in a £12 million move a year ago, headed against the post from five yards with Martin stranded but just after the hour, he made no mistake from similar range to head in Downing's cross.
The opportunities continued but the 7,000 fans that had made their way from Cumbria finally got the opportunity for a pitch invasion with 10 minutes left, when Jason Walker turned in from close range after Steve McNulty flicked on Mark Boyd's corner.
Middlesbrough successfully repelled a barrage of balls into the box and even though Downing should have added a third and Alves hit the post again in the final minute, but having had in the region of 30 efforts on goal, it was far from convincing.
Barrow co-manager Dave Bayliss said: "If they'd taken their chances it could have been double figures but they didn't and that gave us the opportunity."
Middlesbrough: Jones, McMahon, Wheater, Huth, Pogatetz, Johnson, Walker, Digard, Downing, Alves, Aliadiere (Emnes 34), Emnes (Mido 84). Subs: Turnbull, Taylor, Riggott, Sanli, Bates. Booked: Digard. Goals: Alves 23, 62. Barrow: Martin, Pearson (Bond 52), Jones, McNulty, Logan, Henney, Joyce, Boyd, Paul Brown, Walker, David Brown (Curtis 65). Subs: Deasy, Rogan, Tait, Sheridan, Bayliss. Booked: BoydGoal: Walker 80. Referee: Mike Dean (Wirral).