Projectiles rained down from the 60,000 capacity Hungarian crowd towards Raheem Sterling after he opened the scoring in the 55th minute.
Earlier, English players had been booed when they took a knee prior to the game in defiance of racial abuse, while Sterling and Jude Bellingham were the target of chants at Puskas Arena.
There have been claims that those chants were racist in nature, with suggestions the players were taunted like monkeys.
England boss Gareth Southgate told Sky Sports: “We weren’t conscious of it on the side. I don’t know if the players on the pitch were. But everyone knows what we’ve spoken about for two or three years.
“They know what we stand for as a team and we have to hope we can continue to eradicate racism not only in football but from life in general.”
The English FA released a statement, requesting a FIFA investigation into the incidents.
Along with Sterling’s goal, Harry Kane, Harry Maguire and Declan Rice all scored.
Elsewhere, Spain took an early lead from debutant Carlos Soler but defensive issues cost them as they lost 2-1 to Sweden.
Real Sociedad striker Alexander Isak swooped on an errant pass in Spain’s defence to level before Viktor Claesson scored a 57th minute winner.
Euro 2020 winners Italy were held 1-1 by Bulgaria in Florence, despite Federico Chiesa’s 16th minute opener as Ascoli forward Atanas Iliev equalized.
Germany were profligate in front of goal but found the vital strikes from Timo Werner and Leroy Sane in a 2-0 triumph over Liechtenstein.
Romelu Lukaku scored a double as Belgium routed Estonia 5-2 after trailing early while Poland cruised past Albania 4-1.