In a pre-recorded message, broadcast on international television before the match - which the United States lost 2-1 - Mr Clinton said he and the Iranian President, Mohammad Khatami, worked to encourage more people-to-people exchanges.
Mr Clinton's brief message was the latest, and by far the most public, step in a slow warming of US policy towards Iran. He told the Iranians he hoped "the match can be another step forward to ending the estrangement between our nations".
It is not known what impact the message had on the millions of jubilant Iranians who poured onto the streets of Tehran in the early of this morning to cheer their triumph over a political arch-rival.
Crowds of men, women and children gathered in the city centre waving flags and chanting: "Iran, Iran, Iran." Cars blew their horns in time to the revellers' shouts, ignoring pleas from police to lower the noise.
Mr Clinton's message was the latest step in a slow warming of US policy towards Iran. Last week, the US Secretary of State, Madeleine Albright, skewed a speech on Asia policy towards Iran, to say that it was time to bridge the gap and develop a "road map towards normal relations".
Her speech was the US administration's first considered response to a television interview given by President Khatami on CNN more than four months before, in which he had called for an end to the hostility with the US and proposed, as a start, more non-diplomatic exchanges. US policy was to call for a resumption of diplomatic relations before further exchanges.
The timing of Ms Albright's address, just a few days before the World Cup tie, was seen in some quarters as an attempt to defuse what would inevitably be a tricky diplomatic encounter.
Toulouse braced, page 4
World Cup, pages 27-32
Review, page 4