England were forced to come from behind to earn the draw and then had to play 15 minutes with 10 men after captain Andre Wisdom was shown a straight red card.
"We said at the beginning of the week that we won't go into every game and not make mistakes or not go behind, so it's how we respond to those things that matters," Southgate told PA.
"We've got to keep doing the right things and we kept passing and probing. We kept doing that when we went down to 10 men as well, which was really pleasing."
England currently sit second in their Under-21 qualification group, four points behind first-placed Finland with two games in hand.