England have reported an on-field incident to the match referees after Poland's Kamil Glik appeared to pinch Kyle Walker's neck.
Both sets of players clashed at half-time during the World Cup Qualifier, with incensed Harry Maguire eventually booked along with Glik.
FIFA will now look into the matter to understand the full facts of what took place.
"We're getting to grips with what that was," Gareth Southgate told BBC Radio 5 Live. "There's been a report put in and we need to find out a little bit more about what's happened. At the moment we're still gathering all the evidence so there's no point in me speculating any further."
Asked again about the incident in the post-match press conference, Southgate added: "We're trying to find out exactly what happened and when we know more then we will let people know."
Southgate defended his decision not to use any of his substitutions after England conceded a stoppage-time goal in the 1-1 draw in Warsaw.
The England boss made 11 changes from Sunday's win over Andorra, reverting to the starting side he put out for last Thursday's win in Hungary for the trip to Poland.
After Harry Kane's strike had put the visitors ahead, Southgate stuck with those players, despite England retreating in the latter stages of what had been a physical and, at times, frantic contest.
His options on the bench included defenders Reece James, Trent Alexander-Arnold, Conor Coady and Kieran Trippier.
"We were very comfortable and in total control so it would have been making substitutions for the sake of it really, and that can disrupt the rhythm we had," Southgate told Sky Sports News.
"I have absolutely no doubt that will be questioned but we didn't see that was needed."