The England duo were subjected to racist abuse in England's 4-0 win over Hungary on Thursday.
Sterling having scored the first goal of the game was racially abused by the Hungary fans when he celebrated his goal infront of them.
Bellingham though did not feature in the game but got his share of the abuse as he received monkey noises from those supporters while he was warming up on the touchline.
Being pleased with how his players and the entire squad comported themselves, Southgate stressed;
"I can only reiterate that the players are incredibly mature in the way that they deal with it.
"I think they feel supported by their team-mates which is very important to them and their team-mates must recognise how challenging it can be for our black players and how disappointing it is that in the modern world we continue to have to answer these questions because of the incidents that happen."
"We can only continue taking the stance that we have done and hope that we continue to send the right messages not only to people in football but across society and that everybody keeps progressing.
"We know that it's going to take time and that it feels very slow for everybody but we have to keep fighting that battle."
FIFA have started an investigation into the case in the Hungary capital but England are now concerned with their next World Cup qualifier against Andorra on Sunday.
Hungary were charged by European football's governing body UEFA during the Euro 2020 tournament for racist chant against France and Portugal in Budapest earlier this year.
The Magyarok were told to play two games without fans but the sanctions are yet to be operative until next year's Nations League because the World Cup qualifiers fall under FIFA competition.
