Boro fans were left frustrated after their team had equalised as the hosts displayed little ambition to push on and grab the winner.
But Southgate defended his side afterwards and revealed their approach was something they had discussed prior to the game.
"We will never settle for what we've got but I think sometimes circumstances influence the players," he said. "We spoke beforehand about having no regrets and at times like this the players have to keep going forward and not be frightened to lose.
"We have to take a chance and be prepared to be bold, and if you are bold you might get more than you think or you deserve."