Maguire was jeered before kick-off before England went on to win 3-0 thanks to goals from Ollie Watkins, Raheem Sterling and Tyrone Mings.
The 29-year-old has endured a difficult season at club side Manchester United and has often been scapegoated for the club's poor form.
But Maguire has always been a pivotal part of the England set up under Southgate and he played key roles in the Three Lions' run to the World Cup semi-finals in 2018 and the final of EURO 2020, where he was named in the team of the tournament.
"I thought the reception was a joke, an absolute joke," manager Southgate said. "The way he has performed for us has been absolutely phenomenal.
"I don't get it. We're either all in this together or we're not. He's in an England shirt and [...] you support a player in an England shirt regardless.
"When you've played at the level he has for us and put the performances in he has, it should be total commitment behind him. I don't get it at all.
"His performance was pretty faultless really. He stepped out from the back really well for his first goal, was involved in the second one too.
"The team are totally united. We recognise everyone has difficult moments, but he's a top player and he will come through it.
"They are real England fans and some are influenced by whatever – social media or players that played previously who are influencing opinion.
"The club situation is obviously very difficult, but he's in an England shirt. I remember decades ago a few players being booed in an England shirt, and it's never been acceptable to me. Fans should always get behind their team."
