England's players were wished good luck by their partners on social media as they started their trip to Russian Federation.
"I think there was a shift in public opinion in November when we brought in some of the younger players", said Southgate.
Despite the improving relations with the supporters and more optimistic mood within the country, few associated with England expect the team to win the World Cup on July 15.
"I'm confident it won't happen (again) - I won't say 100 per cent because you never know in football - but in this team we wear our heart on our sleeve".
It comes after the Three Lions spoke to injured servicemen from the Royal Marines in a bid to put the pressure of the World Cup into perspective.
He said: "I've talked before about there being a disconnect between the supporters and the team - and I've felt that there's different ways to bridge that".
"What people have seen is the way we want to play - and we definitely want to be an intelligent team in terms of tactical approach and dealing with different stakes and stages in games".
The Three Lions have often capitulated in shootout scenarios at major worldwide tournaments having been knocked out of the World Cups in 1990, 1998 and 2006 on penalties. "But for us it's to play attacking football, to score, and that's important", he said.
"I'd love to win everything with Tottenham, but for me personally the World Cup outweighs them all".
"We just didn't know what to do to get back in the game when we were behind because we just hadn't planned for it".
"We're proud to be here, we will work hard, be energetic".
"We played a behind-closed-doors game in France [at the 1998 World Cup] with Glenn [Hoddle] against local opposition, which I thought worked quite well".
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