The Boro boss admitted there could be some short-term difficulties in order to secure the long-term future of the club.
"It's very simple for me. He's [Gibson] someone who cares about the long-term of the club and that's why financially we've had to do certain things this year," he said.
"Now that's left us a huge challenge in terms of staying in the league but it's a challenge we can win.
"But long-term it might have been the most important couple of years for the long-term future of the club."
Southgate said he was "very confident" Boro - who host Wigan on Saturday - could get out of relegation trouble, despite being locked on points with bottom-placed West Brom and earning just five league wins all season.
"What's pleased me in the last few weeks is the improvement in performance and obviously everyone outside the club is going to focus on results and the position that we're in," he said.
"But to get those results we're going to have to play well, we're going to have to play our way out of the position that we're in."
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