The booing was drowned out by applause from most of the stadium, with the majority supporting the anti-racism act.
England won the match 1-0 courtesy of Bukayo Saka’s 56th-minute winner and will return to the Riverside on Sunday for another friendly match against Romania.
When asked about the booing after the match, Southgate said: “I did hear it, it’s not something on behalf of our black players that I wanted to hear because it feels as if it’s a criticism of them.
“I think we have got a situation where some people seem to think it’s a political stand that they don’t agree with, that’s not the reason the players are doing it, we’re supporting each other.
“I was pleased that it was drowned out by the majority of the crowd but we can’t deny the fact that it happened.
“I think the most important thing for our players to know is all our players and all the staff are fully supportive.
“I think the majority of people understand it, I think some people aren’t quite understanding the message and I suppose we are seeing that across a number of football grounds at the moment.”
Around 8,000 fans attended the match at the Riverside, the ground's highest attendance since March 2020 due to the Covid-19 pandemic, with the majority creating a positive atmosphere.