With a number of key performers absent, including Jonathan Woodgate, George Boateng and Gary O'Neil, Southgate put his faith in youth products at Ashton Gate.
Southgate said: "We played in a controlled manner and I was pleased with the way we responded to going behind. It would have been easy to panic but we kept passing the ball.
"The second goal was really pleasing. It was great to see a centre-half charging forward into the box and I thought young Ben Hutchinson did a very good job for us up front in his first start.
"Lots of people were expecting Bristol to beat us and if you get it into your own mind that there is a chance of an upset then you can build it up into a bigger problem than it is.
"I wanted us to attack the game and be positive. We fielded as strong a team as we could as we had a lot of players missing and we were down to quite young professionals so great credit to them."