Boro were a class above the Premiership new-boys as goals from David Wheater and England winger Stewart Downing gave them a deserved first home victory.
"I thought we set about it in the right way," said Southgate.
"I thought we had loads of energy, movement, pace. We created a lot of chances.
"I was delighted in the second half at 2-0 up we didn't take our foot of the gas and we kept going forward but at the same time we did not concede too many chances to them.
"It was a good healthy professional performance and I think we played very well."
Having drawn 2-2 with Newcastle last Sunday and beaten Northampton at the Riverside in a midweek Carling Cup tie Southgate was half-expecting is team to be slow out of the blocks but they proved him wrong.
"That was spot on today. I couldn't have asked any more from my players," he added.
"We've had three home games in a week, which is often difficult, and the performances in all of them have been good, the level of fitness has been good.
"It is important when you play like that to win matches and it was important to get our first home win.
"If you play as well as that you need to get the results."