The BBC quoted a Leicester City spokesman as saying that while they had congratulated Millwall on their victory, the behaviour of their fans was unacceptable.
"Following receipt of numerous complaints relating to the constant abuse, provocation and intimidation of our players, staff and supporters ... we have registered our dissatisfaction with the FA," he said. "We are awaiting their response."
Millwall expressed disappointment that Leicester did not raise the issue on the day of the match.
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"We have been made aware of these allegations today and are extremely disappointed that Leicester City, as is the professional protocol in such instances, did not raise them on the day of the game itself," a spokesman for the League One club said.
(Reporting by Simon Jennings in Bengaluru; Editing by Peter Rutherford)
