Jan Cheek, representing the Legislative Assembly of the Falkland Islands, said the Argentine government was "deeply worried about our referendum" and criticised Mr Timerman's decision not to talk to them.
She said: "Sadly, there was an empty chair in the room, as the Argentine foreign minister declined to attend. We are disappointed, but hardly surprised.
"Argentina prefers to disregard our existence, rather than engage constructively with the people who have lived on the Falkland Islands for so many generations.
Mr Hague said it was a "shame" the Argentine foreign minister had not attended the meeting and pledged the British Government's full support for the referendum.
He said: "As I have said before there is no way such a conversation could have taken place without members of the Falkland Islands Government being present, especially given the current Argentine government's behaviour towards the islanders. It is, and must always be, for them to decide their own future."