The incidents in the UK took place around England's 2-1 extra-time win over Norway at the World Cup on Saturday, with more than 100 arrests.
The situation was in contrast to fans attending the quarter-final in Miami.
"The atmosphere during the game was passionate but friendly, with no animosity between fans at the end of the match," said chief constable Mark Roberts, the head of the UK Football Policing Unit (UKFPU).
"It's a real shame that the same cannot be said about the behaviour of fans back home here in the UK."
Extended pub licensing hours allowed supporters in England and Wales to the entire Norway game, which kicked off at 22:00 BST.
The Home Office said the extended hours would also apply to any further England matches, including potentially the final, ensuring venues can stay open until 30 minutes after the final whistle.
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Roberts previously praised England fans in the US for their conduct and has called for that to be mirrored domestically when the side take on Argentina in a World Cup semi-final at the Atlanta Stadium on Wednesday (20:00), in a game that will be shown live across the BBC.
"This behaviour really is disappointing. Domestically this tournament is the worst one we have seen for number of incidents and arrests.
"If we can have 40,000 fans together in Miami with no trouble, then why can't fans follow their exemplary behaviour and do the same back home?"
He added: "Ahead of Wednesday's game I would urge fans back home to follow those leading by example in the US - enjoy the game and atmosphere, go out and have fun but do so without causing problems for yourselves and others."
Meanwhile, the Atlanta Police Department has "enhanced its citywide public safety and security posture" prior to England's game against Argentina.
It added: "Additional personnel and resources are already deployed and will continue to be strategically assigned in and around the event venues, entertainment districts and other high-traffic areas to help ensure a safe and enjoyable experience for everyone.
"These proactive measures are designed to protect the public, deter criminal activity and ensure residents and visitors can safely enjoy this historic event."
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