Thailand missed out for the first time in 22 years, making it a miserable start to former England and Manchester United captain Robson's international coaching career.
Having failed to make an impression since taking over from compatriot Peter Reid in October it is uncertain whether Robson, who is under contract for four years, will still be in charge for the 2014 World Cup qualifying campaign.
"It is very upsetting not to be in the finals of the tournament," Robson told reporters.
"The team has had many problems since I arrived here, I did my best to resolve these problems but in the end I could not find a solution to the problems of my offence."
With Group E winners Iran already through to the Asian Cup finals in Qatar, Jordan took second spot with a 2-1 win over bottom team Singapore.
Thailand, who finished third, struggled to make headway against a full-strength Iranian side lifted by a sparse but vociferous crowd at Tehran's Azadi Stadium.
Former Asian player of the year Ali Karimi was instrumental in most of Iran's attacks and came close to scoring several times, teaming up with Ehsan Hajisafi and Nekounam to heap the pressure on the visitors.
News of a Singaporean equaliser in the other group match led to a brief rally by the Thais but that was short-lived when Jordan restored their lead and Iran regained control with a torrent of attacks that led to Nekounam's decisive header.
