Following Sunday’s defeat by Spain, Southgate took less than 48 hours to announce he was stepping down as England boss after eight years in charge.
“It actually wasn’t too much of a surprise to find out he’d gone,” Schumacher added.
“I always felt if we didn’t win this tournament Gareth would fancy a new challenge but he has done an unbelievable job considering where England were as a team, the lack of connection with the fans when he took over and the pressure of doing that job.
“We’ve reached one World Cup semi-final and lost in two Euro finals – once on penalties and the other to a goal in the last few minutes against the best team in the tournament. And it all could so easily have been completely different. But for very small margins, he could have been the best England manager ever.
“He certainly has all the right traits to aspire to about being both a good man – and a good manager.”
Schumacher, who took his first steps in coaching alongside his former team-mate and fellow Liverpudlian Ryan Lowe, first at Bury, then at Argyle, was promoted to the Pilgrims’ hot seat in December 2021 when Lowe left for Preston.
Originally intending to go to Deepdale alongside Lowe, Schumacher was persuaded to stay at Plymouth.
But, just prior to that, they had both shared an online video session with Southgate.