The Three Lions will take on Switzerland in a Euro 2024 quarter final on Saturday.
As he prepares for his 100th game, Southgate may be aware that he is no longer popular among the supporters.
Manchester City defender Stones said: “I’ve only heard about the criticism he’s been receiving. I saw some fans after one game throwing bottles in his direction. I’m sure that will have motivated him that bit more.
“Everyone who has spent time with him and know him as a person, knows how hard he and his backroom staff work. So definitely we want to win for them, ourselves and our families and everyone in the nation.
“He is very clear in what we can achieve as a nation. The great attributes and qualities he has as a manager is that he is simple and clear to the players. That has not always been done.
“So to be able to be here and try and make a mark in this tournament is important and we have that goal at the end which is to try and do something which has never been done before.”