The 28-year-old defender scored one of England’s two successful penalties in the shootout loss to Italy in the final of Euro 2020 on Sunday (11.7.21).
And he believes England manager Southgate deserves the chance to lead the side at next year’s World Cup in Qatar after doing an "amazing job" up until to now.
He said: "To reach the final of Euro 2020 is a great achievement, but we now have to take that next step and be convincing in these big games and these big moments.
"I think Gareth has done an amazing job and deserves the credit, and deserves another opportunity.
"I think the way Gareth handles the squad, and the togetherness of the squad, is a big reason why we have been on this journey together and where we have ended up.
“The relationship we have got from fans to players, to media and the staff.
"I think we feel we are all on this journey together and that is really important.
"We all want the same thing.
"The past has made it difficult to do that, due to the small number of knock-out games we had won.
“We had not won enough.
"Over the last two tournaments we have done that."
And with Southgate earning a reputation as one of football’s nicest men, from his playing days with Aston Villa, Middlesbrough and Crystal Palace right through to his managerial career, Maguire doesn’t want people to confuse niceness with weakness.
With the former Sheffield United and Leicester City player saying Southgate does have a “ruthless” side and isn’t “scared of anything”.
He added: "I think he can be ruthless. He has that side to him. He makes big decisions and is not scared of anything."