Tottenham fullback Danny Rose was allegedly subjected to racial abuse from Montenegro fans during England's Euro qualifying win on Monday night.
The FA are now set to speak to their players and compile evidence before reporting the incidents to Uefa.
Southgate said: "I definitely heard abuse at Danny Rose when he got booked at the end of the game.
"There's no doubt in my mind that happened.
"We'll make sure it's reported officially. That's not acceptable."