Southgate claimed that despite ranking fourth at the tournament, England were "not a top four team yet", though he reiterated he was proud of his team's progress during the tournament.
Petrovic said that sports rivalry was also strong among the Balkan nations even while they were all part of the former Yugoslavia, when it was also rare to see Serbian or Croatian teams support one another.
"We now have players who I think can stand on their own two feet in the Premier League", said Southgate.
"We have cleared a lot of hurdles and that can only benefit the team and the nation generally to help us move forward".
"Today was always going to be a really hard game". We have set ourselves a certain level, want to maintain a high standard until the end of the tournament.
Both teams will line up in Saint Petersburg with a sense of what might have been as France and Croatia prepare for Sunday's final in Moscow's Luzhniki Stadium, but they will want to leave Russian Federation on a high. The future can be very good.
Southgate concedes Raheem Sterling was among a couple of exhausted players that he perhaps should not have fielded in the 2-0 third-place play-off defeat to Belgium, but any major regrets will take a longer time to compute. We have some minor injuries, minor problems, and I hope my players will be ready. "We try and find that balance of an environment where people can improve and learn and get better and recognise at the time you have to make selection decisions as well".
Comfortably the most experienced member of England's World Cup squad, the manager has had open and honest dialogue with the 32-year-old about his role.
"We will analyse all of this and we will make sure that the Croatians are not in good shape, and that we can block their best player and their best plan of attack". If they're not we have great players on the bench who are raring to go. We have this togetherness, this unique unity - not just in football.
Kylian Mbappé has had a superb World Cup, and was in great form again against Belgium, tormenting them with his pace and trickery.
In a rare recent interview he said: "I never relax because if you relax in football your level drops and it can be hard to get back into it". Yes, not only is it the World Cup final, but it is also the climax of our predictions game.
Belgium's Romelu Lukaku has four goals in Russian Federation, with the French pair of Antoine Griezmann and Kylian Mbappe both on three. It can't just be that I pick a group of players to get a result today.
"We have to put that game behind us", Rakitic said.
We'll have to see how the teams look when starting lineups post, but for a second time this cup, Belgium is the favorite against England and should continue to be, unless Belgium rests its stars and England players its big boys.