Ross Barkley and Raheem Sterling scored two apiece as the Three Lions recovered from their defeat to the Czech Republic in impressive style and moved to within touching distance of securing a spot at Euro 2020.
But the game was stopped twice due to racist chanting from the stands in Sofia – England debutant Tyrone Mings having initially notified the officials and captain Harry Kane remaining in regular dialogue.
Security ejected a group of Bulgaria supporters before half-time and, despite a match abandonment appearing on the cards, England played on to mete out further punishment to its overmatched opponent.
"I have to say that the officials were on to everything very quickly. We reported everything immediately when we heard things," Southgate said. "We had constant communication with the fourth official and the referee.
"I was in contact with the players all the way through the first half in particular and then again at half-time.
"We know it's an unacceptable situation. We've managed to make two statements really, by winning the game but also by raising the awareness of everyone to the situation.
"The game was stopped twice and I know for some people that won't be enough but I think as a group we were on board with that process."
Speaking to Sky Sports, Southgate explained his England squad had prepared for such an eventuality at Vasil Levski National Stadium, where some sections of the grandstands were closed for the match as a punishment for previous racist behaviour during Bulgaria's June qualifiers against the Czech Republic and Kosovo.
"I'm incredibly proud of all my players and staff," Southgate said. "We prepared for this game on the field and off the field.
"The whole group have been united in where they stood on what might happen, where we were during the game, at half-time and we've spoken again at the end.
"Our players feel well supported. It's such a difficult area because I know not everybody will agree that we've gone far enough. But I still believe we've made a huge statement, the game was stopped twice. I don't believe that's a situation that's happened before in international football.
"For me, an even bigger statement was the way our players played. We've got players who've gone through something they should never have to experience and they've come off with a smile on their face because of how they played.
"They always want the story to be about football but they've also been part of something that I think will be bigger."