"I am pleased for them at the end of what has been a difficult week. They responded with a calmness and unity," Southgate said.
"Some supporters have expressed their displeasure, which I have accepted. Our job is to manage the club through difficult times.
"It's easy to manage when things are going well but the margins between success and failure are so small.
"I selected Leroy Lita to play against his old club because you just knew what was going to happen.
"He missed pre-season so he is still coming back to sharpness but he was terrific."
Reading boss Brendan Rodgers was bemused at the difference between his side's form in the midweek win at Preston and Saturday's defeat.
"Everything that was good about us in midweek wasn't good today," he said.
"We showed quality to get into the areas we wanted to be in but a mixture of poor decision making and poor final ball let us down.
"We started on the back foot and we were lacklustre and it's difficult to put your finger on it. We need to show courage and bravery at home to make things happen and we didn't do that today."
Reading are still without a home win since January 27 and have scored just twice at home in the league this season, fewer than any other side in the Championship.
In the opening minute Reading goalkeeper Adam Federici just managed to beat Lita in a race to the ball, then the Boro striker saw an effort blocked by a defender and almost immediately sent in a header which was saved by the Royals goalkeeper.
Boro's opening goal came after 12 minutes when Adam Johnson's corner was headed in by St Ledger, although Lita later claimed he had got the final touch.
Reading's chances were few and far between with Jem Karacan's drive blocked by team-mate Darren O'Dea and Jimmy Kebe's cross headed wide by Brian Howard.
At half-time Rodgers brought on Noel Hunt for Kebe, but Boro were still on top and Lita still a threat.
And 10 minutes into the half Lita scored the goal he had been threatening all game.
He beat Karacan in the centre circle, span away from O'Dea and ran on unchallenged before shooting hard and low past Federici's despairing dive.