Harry Kane settled the contest with his 59th international goal nine minutes from time as England supporters continued to chant Maguire's name in response to sustained abuse.
Maguire was also cheered by Arsenal fans when appearing as a substitute for Manchester United at Emirates Stadium earlier this month and Southgate believes the negativity is the product of unfair coverage.
"From a Scotland fan's point of view, I get it and I have absolutely no complaints with what they did," began Southgate. "It is a consequence of ridiculous treatment of him for a long period of time, frankly. I think our fans recognised 'OK, there might be a bit of heat from our own supporters but we're not going to have it from others getting into him.'
"But it's a joke. I've never known a player treated like he is, not by the Scottish fans but by our own commentators, pundits whatever it is. They've created something beyond anything I've ever seen. He's been an absolute stalwart in the second most successful England team in decades.
"He's been an absolutely key part of that. I've talked about the importance of our senior players, he's been crucial amongst that. Every time he goes on the field, the resilience he shows, the balls he shows is absolutely incredible. He's a top player, we are all with him and our fans were brilliant with him tonight."
He added to beIN Sports: "The reaction tonight is a consequence of idiots really from our side who have created that environment."
Asked how Maguire was, Southgate continued: "He's good, he's great. We've had a good win. He's been a big part of that. He's gone and spoken with the media because that's the sort of lad he is. He's fronted up as he always does. Enormous credit to his character."