Maguire has endured a miserable run of form in recent times. He was dropped by Red Devils boss Erik ten Hag following the 4-0 defeat at Brentford in August.
However, Southgate started the 29-year-old in clashes against Italy and Germany in the UEFA Nations League during the international break.
Maguire failed to repay that faith against the Germans. He gave away a penalty shortly after a misplaced pass, before losing possession for a second goal during their 3-3 draw.
The Manchester United captain has been widely panned for his display at Wembley, but Shaw has stepped in to defend his fellow defender. The left-back, who has also been dropped by his club, told BBC Sport:
"Harry is an amazing player, an amazing character. He's taken a lot of stick, probably more than I've ever seen before in football. He never hides away, he's always there. You can have people who can hide away and not want to be in the spotlight. He keeps putting himself in the spotlight, it shows the strength and character he's got."
"Everybody knows he's an unbelievable player. At the moment the confidence might not be there because it could feel like the whole world is against him."
Shaw claimed that Maguire has the team's support and that fans need to support him as well. He said:
"It's tough for him, but us as players and staff are all behind him because he's a very important player. It shows Gareth's trust because he's played in both games, and look at the Euros what he's done. People need to understand he's a big part of the England team and have to accept it."
Former England striker claims he feels sorry for Harry Maguire
Following another disastrous display, many have begun to question whether Maguire should be heading to the World Cup in less than two months time.
Former England striker Chris Sutton was questioned by BBC Sport during the game if he felt sorry for the England defender, to which he replied:
"Yes, totally, I really do."
Sutton went on to describe Maguire's mistakes for the first goal as "horrific," saying:
"Blimey, you wouldn't have a heart if you didn't feel sorry for him. The second goal, it wasn't comical, but you'd have to laugh or you'd cry for him. Gareth Southgate has a huge decision to make."
"If Erik ten Hag is watching the game he's thinking 'blimey, can I ever play him for Manchester United again?' He's a player whose confidence is shot to pieces."
The former Leicester City man has started just three matches for Manchester United so far this season and the club have lost all of them.
However, he will hope to get some game time under Ten Hag to improve his form and fitness ahead of the World Cup.