Heaton was part of Southgate's staff at the Euros this summer and was surprised by the negative reaction from fans during a difficult group campaign.
"I do. I think he has changed the feel and expectation of England football. It’s rare to get a full squad of players wanting to win for the manager. He’s a leader you want to follow," said Heaton.
"I was involved from the start of that tenure when it changed from Big Sam (Allardyce) to Southgate, and since that point the England set-up has always felt really positive. But I think that first game (against Serbia at the Euros) felt different. It felt like the narrative changed.
"Getting booed in each half, pretty much in every half all the way to the semi-final, it wasn’t easy. That probably took its toll on him — the sort of guy who would only be wanting the optimism to try and win it, giving everything he’s got for it.
"I was caught a little bit by surprise (by Southgate’s decision to quit), but when I thought back and reflected on it, I could see it from his point of view. Gareth is his own man in terms of what he wants."