The Three Lions players were incensed by an incident as they headed off the pitch at Stadion Narodowy in Warsaw on Wednesday night.
Television cameras did not pick up clear pictures of what precisely happened to spark the melee that involved nearly every player on the pitch, but subsequent footage appeared to show Poland defender Kamil Glik pinching Kyle Walker’s neck.
Referee Daniel Siebert booked both England centre-back Harry Maguire and Glik following the heated row.
But afterwards Gareth Southgate confirmed England were investigating, with the incident reported to the refereeing team and match delegates.
It is now up to Fifa to look into the matter and establish the full facts of what took place.
“We’re getting to grips with what that was,” 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.”
Harry Kane added: “There was an incident just before half-time which has been reported to the FA guys. They’re taking care of it and investigating it and we’ll go from there.
“Allegedly it was something that was done, not said. We haven’t had chance to look at the footage.”
Meanwhile, Southgate admits England missed the chance to all but guarantee World Cup qualification in Poland.
Damian Szymanski’s stoppage-time equaliser ended the Three Lions’ 100 per cent record in Group I but they are still four points clear at the top.
Southgate reminded his players that there is still work to do after the 1-1 draw but hailed their response to losing the Euro 2020 final in heartbreaking fashion in the summer.
He said: “Across the 10 days they have been fantastic. You couldn’t be sure what reaction there would be after the summer.
“We knew that today if we could win the game we were pretty much in Qatar. That isn’t the case, there is still work to do.
“We could have been in an even stronger position so that is disappointing, but I can’t fault the players for the way they’ve responded since the summer.”
Kane fired England ahead in the 72nd minute with what looked like being the winner until Szymanski’s goal.
The England captain said: “It was a a tough one to take right at the end. I thought we handled the game really well. We got ahead and were seeing the game out well.
“When you are away the pressure builds. We are still five points clear at the top.
“It’s been two tough away games, we are five clear (of Poland) and in a great position.”