Photographs showing certain supporters with black make-up on their faces circulated on social media, sparking suggestions that a minority of the European team's fans were displaying racist behaviour.
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A spokesperson from Fifa told a media briefing that the claims will be investigated.
"We always take any evidence or submissions to our disciplinary committee. It is the disciplinary committee that will meet," she explained. "If they see any grounds they will open proceedings. Then it is up to the disciplinary commission to take the decision."
Prior to the match, there were reports that some German fans were asked to take down banners that displayed political messages, although these were of an undetermined nature.
Football Against Racism in Europe (Fare), which was established in 1999, had previously expressed concerns over certain banners displayed by fans from Russia and Croatia during this competition, and Fifa has confirmed that they will act against perpetrators of such incidents.
"If something like a banner is spotted, it will be removed. If something is not spotted and someone has images of it, then if anyone submits evidence of those things then our disciplinary committee will consider it. We clearly have zero tolerance of any form of discrimination."