Adnan Hamad was held for around four hours and questioned by officials after arriving with his team from New Zealand in preparation for Jordan's World Cup qualifier against Australia next Tuesday.
The Jordanian Football Association said their delegation had completed all the necessary paperwork and requested clarification from Australia's football governing body.
Foreign Minister Bob Carr called Jordan ambassador Rima Ahmad Alaadeen as a "diplomatic courtesy" after the incident, a spokesman from Carr's office said on Friday.
"It was an expression of regret for any embarrassment or inconvenience that may have been caused," the spokesman said but stopped short of saying that the call was an official apology.
"It was conveyed to say, 'We hope you don't think that it's a reflection of your welcome in the country'."
A spokesman for Australia's Department of Immigration and Citizenship said the coach had been referred by customs officers to immigration officials to "confirm his immigration status".
"From time to time they might stop and question someone to confirm this," he said.
The JFA complained that no-one had been made available to help them with their entry into Australia, as agreed with Football Federation Australia.
The FFA said they had sent two personnel to meet the Jordan delegation, but had no control over customs.
Australia central defender Sasa Ognenovski gave a wry smile when asked on Friday about the incident.
"Maybe customs were trying to hold them back or something," he said in Melbourne.
"Maybe (Australia coach) Holger (Osieck) had something to do with it."
Jordan and Australia are locked on seven points in Group B of the final round of Asian qualifying for the 2014 World Cup finals in Brazil, with the Socceroos in third spot on goal difference.
Japan (14 points) have already claimed one of the two automatic qualifying sports for the finals with second-placed Oman on nine points, though they have played one more game than Australia and Jordan.
The team finishing third in the five-team group can still qualify for Brazil, but must win a two-legged play-off against the equivalent finisher in Group A before another play-off against the fifth-placed team in South America.