The programme, aired last Monday three days before the vote in Zurich on who would host the tournaments in 2018 and 2022, accused four members of FIFA's executive committee of taking bribes.
Ultimately, Russia was named the host of the World Cup in eight years' time, after England picked up just two votes in the first round of balloting.
England 2018 chief executive Andy Anson subsequently claimed that he had been told the FIFA president Sepp Blatter referred to the "evils of the media" in a speech to the committee just before the vote.
It was suggested that the negative impact of BBC One's Panorama and UK media coverage in general had been a "big influence" on England missing out.
Speaking on The Andrew Marr Show on BBC One, Thompson said that it had been the "right" decision to screen the edition of Panorama, because it contained "significant information about matters of very serious public interest and public concern".
Thompson also said that the information was received by the Panorama team just a few weeks before broadcast, and they checked the allegations thoroughly before proceeding.
"They spent time checking the provenance of this information, putting a number of specific allegations to the people involved, as we must do, and when the programme was ready to transmit, we transmitted it," he said.
"I have to say that I believe that in the end, although I understand that there are often reasons to believe that transmitting a programme might be impolitic or inconvenient, if you believe that you have a matter of real public concern to broadcast, there have got to be overwhelmingly powerful reasons for not broadcasting.
"I believe we were right to broadcast and I believe we have very strong support from the British public in broadcasting."