United equalised late on through Wayne Rooney but Boro could quite easily have taken maximum points when they almost grabbed the winner in stoppage time when substitute Sanli Tuncay was denied by United keeper Edwin van der Sar.
"The team performance was excellent. We answered most of the questions and had them on the back foot for the majority of the game," Southgate said after the 2-1 draw at The Riverside.
"We were up against a team that are both outstanding to watch and to test ourselves against and we had them rattled.
"We've now been to Chelsea, Arsenal, Aston Villa and given a good account of ourselves."