Riot police had to break up skirmishes between rival fans before the start with some England supporters appearing to be in a section for home fans with no segregation.
UEFA said in a statement on Wednesday that the LFF also face proceedings over ticketing and blocked stairways.
"We were naturally concerned to witness scenes of disorder in Lithuania," the FA said in a statement on Twitter.
"However, we must be clear that these incidents did not happen within the official England Supporters Travel Club area, where supporters who had bought tickets from The FA were housed.
"We would encourage the authorities to identify anybody involved in disorder and deal with them appropriately through the criminal system and with banning orders. We will, of course, fully cooperate with Uefa."
England won 3-0 to make it 10 wins from 10 in Group E ahead of next year's European Championship in France.
(Reporting by Justin Palmer and Ken Ferris; editing by Amlan Chakraborty)
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