"The families expressed their condemnation and resentment at the recklessness of the Bulgarian nation when the Bulgarian president pardoned the nurses," the Libyan Association for the Families of HIV-Infected Children said.
Last week, Libya commuted death sentences against the five Bulgarian nurses and Palestinian doctor to life in prison following a financial settlement of $1 million each to 460 HIV victims' families.
The medics, who spent eight years in jail, had always said they were innocent and were tortured to confess.
They held a news conference in Sofia, the Bulgarian capital, to give their first full comments on their ordeal.
Ashraf Alhajouj, the released doctor, said: "I thank all the people in Bulgaria.
"I was told I would be transferred to Bulgaria - I said "for sure" as I no longer wanted to be in the Arab world.
"I am really disappointed with the whole Arab world and the how they have taken our case.
"It is a matter of time, I don't know when, only God knows when, and the truth will come out."
The Bulgarian prime minister earlier said Libya's foreign debt to the country may be written off.
Sergei Stanishev insisted the gesture would be part of humanitarian aid measures rather than "paying ransom" for the release of six health workers.
If Sofia writes off the Libyan debt, accrued for arms deliveries and technical assistance during the communist era, the money would be recycled into an international fund set up to help the families of more than 400 HIV victims.
The six health workers were flown to Sofia on a French jet after the EU, which Bulgaria joined in January, brokered a last-minute deal on medical aid and political ties with Libya.
Bulgaria and its western allies have said the six were innocent and suggested that not freeing them would hurt Libya's efforts to emerge from decades of diplomatic isolation.
Nicolas Sarkozy, the French president, is due in Libya on Wednesday and is said to be seeking deeper political and commercial ties with the North African country.