Under Southgate, England beat Malta and Scotland, and drew with Slovenia in World Cup qualifiers before drawing 2-2 in a friendly against Spain earlier this month.
"I feel he does look like the right man for the job. He's young enough to bond with the boys and he's got a relationship with quite a few of the boys through the under-21s," Antonio, who was included in one England squad, told British media.
"We haven't had that for the last few years, someone who is young, who has actually got a relationship with the boys before he's met them so he knows what to do with them, and it shows because he's doing well."
Antonio joins a growing list of players, which include midfielders Jordan Henderson and Adam Lallana, who have publicly backed Southgate for the England job.
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"I'd say he's a great tactician. He wants us to play and the way he trusts the players, he believes the boys can do it, that they are good enough to do it," Antonio added.
"To play for England you have to be quality so it's just about working out the kinks and making the players believe in themselves and have the confidence to play.
"He knows all the players. You can't be around players and not know what makes them tick. That's the difference between him and other managers."
Southgate had expressed interest in taking up the England job on a permanent basis and was interviewed for post last week at St George's Park, according the British media reports.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
