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Featured Image Credit: Sky Sports/ITV
Maguire was booed by England fans during his side's friendly match at Wembley Stadium on Tuesday.
Southgate jumped to Maguire's defence, criticising the supporters who booed the Manchester United defender.
He labelled the hostile reception an 'absolute joke' - but his fierce defence angered Keane who slammed the England manager's comments.
Former Man United captain Keane, who has been one of Maguire's most vocal critics this season, couldn't understand Southgate's post-match interview.
On ITV, he said: "I think Gareth has made it a bigger story than what it is. Every player gets booed. There’s going to be idiots at football matches. England fans have got a lot of idiots.
"And if they’re going to boo Harry Maguire, I think Gareth could have easily said that it’s no big deal. He actually played well, just focus on that."
Keane continued by bringing up an incident involving Raheem Sterling, accusing Southgate of double standards.
"I think he’s made a bigger story than what it is," he added. "And Gareth is almost picking and choosing when to support his players.
"Raheem Sterling had a bust-up two or three years ago, he was bombed out of the squad. He’s left other players out.
"I remember when Harry was sent off [in October 2020] against Denmark. He didn’t really support him - I thought - when he was walking off the pitch.
"So, I think Gareth’s made a bigger story than what it is. Just get on with the game. He played well! And he’ll get fans back onside by his performances, not by people [like Southgate] reacting to a few boos or social media. Forget about it.
"Be big enough and man enough just to get on with the game. And he played well - that’s the most important thing."
Jordan Henderson, Declan Rice and Harry Kane, among others, have backed Maguire, who himself has broke his silence on social media.