Scottish Government officials "scoped" the option of flying with the Prince of Wales but it was ruled out after being deemed a complete non-starter.
Prince Charles is representing the Queen at the service.
However, the Scottish Government was also keen for Salmond to pay his respects in person.
Last Sunday, a spokesperson for the administration was quoted as saying: "Arrangements are not finalised."
Plan A was for the First Minister to attend last Tuesday's memorial service at the 95,000-seater FNB stadium but this clashed with a Holyrood tribute to the former South African president on the same day.
Salmond was also committed to attending the funeral on Wednesday of PC Kirsty Nelis, one of the police officers who died in the Clutha helicopter accident, so going to South Africa was impractical.
Officials then explored the possibility of Salmond flying to today's funeral with Prince Charles.
However, the plan was met with a lukewarm reception after approaches were made.
It is also understood that the First Minister did not receive an official invitation to the funeral.
A Scottish Government spokesman said: "It was not logistically possible for the First Minister to attend [last Tuesday's event] because of commitments in Scotland, notably attendance at the funeral of one of the victims of the Clutha tragedy.
"In any case, the Scottish Parliament had scheduled a debate to commemorate the life of Nelson Mandela, and it was thought more appropriate that the First Minister should lead the debate.
"Scottish Government officials initially scoped a number of options relating to potential attendance at the series of events in South Africa commemorating the life of Nelson Mandela. It soon became apparent that the Tuesday event in the stadium was the appropriate event for politicians from around the world to attend rather than any other event."
A Scottish Labour spokesperson said: "Whether it be a day of great happiness like Andy Murray winning Wimbledon or a day of great sadness like Nelson Mandela's funeral, we know the First Minister likes to make his mark on these occasions.
"Clearly, he has made a valiant effort to be there, even offering to hitch a lift with the Royal Family, but it wasn't to be.
"Even without the First Minister gracing the funeral with his presence, I am sure it will be a remarkable occasion and I am sure Alex Salmond will be able to pay his respects while watching it on the TV like the rest of us."
A spokesperson for the Prince of Wales did not respond to a request for comment. At least 100,000 people saw Mandela's body lying in state in Pretoria over the last three days.
The coffin was then flown from Waterkloof air base in Pretoria in a military aircraft escorted by two fighter jets.
In line with tribal custom, Mandela's grandson Mandla accompanied him on the journey, speaking to the coffin to tell his grandfather he was on his way home to rest. To solemn music, the coffin, draped in a South African flag, began the journey to the burial site.