Montenegro face the prospect of playing future Euro 2020 qualifiers behind closed doors, following allegations of racist chanting during England's 5-1 win on Monday night.
England players, including Callum Hudson-Odoi and Danny Rose, complained of hearing monkey chants throughout the game in Podgorica.
Raheem Sterling celebrated his goal by pulling out his ears, in reference to the complaints made by his teammates.
UEFA has since launched an investigation into the allegations and on Tuesday confirmed that Montenegro would face five charges: setting off of fireworks, throwing of objects, racist behaviour, crowd disturbances and blocking of stairways.
Under Article 14 of UEFA's regulations - which relates to racist behaviour - the "minimum" sanction, should Montenegro be found guilty, would be a partial stadium closure. The case will be heard on May 16.
Raheem Sterling's perfect response to being racially abused by Montenegro fans
Hudson-Odoi, 18, whose impressive first start was overshadowed, picked up an item thrown from the stands after Sterling's goal and called for action to be taken against Montenegro.
"Firstly, very sad," Southgate said afterwards.
"We had an excellent performance and we've got an 18-year-old being interviewed after the game and he's having to respond to what's happened when his evening should be about the joy of his full debut.
England stars racially abused during 5-1 win over Montenegro
"I didn't hear (anything) during the early part of the game, but I'm told there were things in the early part of the game as well.
"But I certainly heard when Danny Rose was booked and it's unacceptable. I've spoken to our players individually. We've got to support them. We will report it.
"But I think that reporting is already in place because so many people in other areas of the ground have heard it. I believe the UEFA delegate also heard it.
England fans love what Raheem Sterling did after scoring against Montenegro
"So, our part will be to make sure that process is followed, but more importantly for me is that the players in the dressing room know that as a group of staff and as an organisation we're there for them. That's the most important thing."
UEFA regulations state that if supporters engage in racist behaviour then "the member association or club responsible is punished with a minimum of a partial stadium closure".
Article 14 also states that additional disciplinary measures can be imposed depending on the situation, while "disciplinary measures may be combined with specific directives aimed at tackling such conduct".
