England players were booed by Hungary supporters when taking the knee in protest against racial injustice ahead of their Nations League clash in Budapest on Saturday.
Hungary were hosting England in what was officially a behind-closed-doors match after being disciplined by both FIFA and UEFA for repeated racist behaviour, including during England's previous visit to Budapest last September.
However, the Hungarian FA said last month children could attend the match at the Puskas Arena. Under Article 73 of UEFA's disciplinary regulations, children up to the age of 14 from schools and/or football academies can be invited to a game free of charge, provided they are accompanied by an adult.
It meant around 40,000 were able to attend on Saturday, mostly children, and after the national anthems, the England players took a knee prior to kick-off, with boos audible from the stands.
Southgate's team were playing their first match of the summer which ended in a 1-0 defeat in Budapest. Before kick-off, the England players took a knee as they have done since the emergence of the Black Lives Matter movement.
In the post-match press conference, Southgate said: "From a development perspective, I want and need the team to be playing in front of supporters. But of course, that's not the point in this instance.
"So I'm torn on what we actually got from that and what the reality should have been. I think that needs some consideration without a doubt. In actual fact the atmosphere when we arrived at the stadium, there were kids lining the streets, it was really friendly."
"That was different with the taking of the knee but that felt like inherited thinking to me. We do it to try to educate and I think young people can only be influenced by older people."
England defender Conor Coady added: "It's massively disappointing. It's important people understand why are doing it. It's not something we want to hear. We want to keep pushing the message."