The documentary, titled Euro 2012: Stadiums of Hate, included footage of Polish fans giving Nazi-style salutes and a group of Asian males being viciously beaten at a match in Ukraine.
After watching the footage, former England defender Sol Campbell was pictured urging British fans to stay away from the tournament, warning that anyone who goes could "end up coming back in a coffin".
But Jonathan Ornstein, the executive director of the Jewish Community Centre in Krakow, has hit out at the BBC's portrayal of the perceived problems in both countries.
In a letter sent to the Economist magazine, Ornstein said that he was "furious" at the way Panorama had "used me and others to manipulate the serious subject of antisemitism for its own sensationalist agenda".
He also urged Rogers to speak to two Israeli footballers who ply their trade at club Wisla Kraków, but was apparently told that "this line of inquiry 'didn't fit their story'".
"The BBC knowingly cheated its own audience - the British people - by concocting a false horror story about Poland. In doing so, the BBC has spread fear, ignorance, prejudice and hatred," said Ornstein in his letter.
"I would urge the BBC to become more aware of its own negative stereotyping of Poles, before it goes pointing the finger of judgment."
According to The Guardian, the documentary has also been criticised by England fan groups, who feel that it gave a misleading impression of the scale of racism in Ukraine.
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Mark Perryman, of the London England fans' group, noted that there had been no reports of racism or hooliganism when England last played Ukraine in 2009, or during recent visits by English clubs to the country on European football nights.
Perryman admitted that the problem existed, but said that it was "very specific" and confined to "inter-club" conflicts on the domestic level.
However, the BBC rejected the criticisms and denied Ornstein's claims that it had refused to interview the Israeli players as this "did not fit" the report's story.
The corporation also said that it had followed up on the attack on young Asian men featured on the programme, and had been told by the Ukrainian FA and police that they were investigating.
"We filmed two games at the stadium and featured both in the programme. The second game was when the attack took place," a BBC spokesperson said.
"At the first game we filmed several thousand people appearing to give a Nazi salute. This was shown in the programme. We also interviewed the local police chief who claimed that this was actually the fans pointing at the opposing fans."