That late goal was not enough to appease some fans in attendance, however, which also proved to be the case during the disjointed display when eventually seeing off minnows Malta 4-0 last month.
Southgate hopes to work as one with England supporters, but says that patience is required from the stands following years of underperforming on the field.
"The players need a chance to grow and they need the country to get behind them," he told reporters. "We are picking up the consequences of decades of disappointment and this group are nowhere near as experienced as those teams.
"We have to keep winning football matches. The more we can play football which excites people and scores goals, the more we will win people over. We have tried to be as open as we can be. We are in an era where it must be difficult for fans to relate to players because of what they earn. But these are good kids, desperate to play for England.
"You are always at tournaments to win football matches but you also have to be thinking what is realistic. I don't know how far the team can go at the moment, but what I do know is that we have got a group of players who I am proud to manage because they want to pull on the England shirt."
England round off their World Cup 2018 qualifying campaign with a trip to face Lithuania in Vilnius on Sunday evening.