The Haemophilia Society, which is seeking payments for members with hepatitis C who become ill, immediately said it would continue its fight.
"We are not surprised at the stand adopted by the Government. They responded in just the same way at the start of the HIV campaign," a spokesman said.
He was referring to the Government's decision in 1990, after a two-year battle, to pay hardship money to haemophiliacs and then to transfusion patients who caught HIV from contaminated blood supplies.
After protracted legal arguments, the Government made £42m available in a trust fund.
The spokesman added: "The society believes there is a strong moral case and will continue its discussions with the Government." He said it was seeking the same financial treatment for sufferers and their families as achieved by the HIV group.
Lady Cumberlege said: "We have great sympathy for those affected, but have no plans to make special payments.
"We have to be careful not to open the floodgates to every case that is made for compensation. If we were to do that, we would get into the US situation where doctors are very frightened now to give a medical treatment for fear of being sued. That would actually finish the NHS and we would all be the poorer."
The minister told the Lords that HIV differed from hepatitis in that it was a very new disease, believed invariably to be fatal, and with devastating health, social and financial effects. But many hepatitis sufferers "could lead ordinary lives for decades".
Lady Cumberlege was responding to Lord Ashley of Stoke, who declared: "Virtually all haemophiliacs who received blood transfusions before 1986 have been infected ... Although no fault is involved, they need payment just the same as those who were infected by the HIV virus through contaminated blood. There is no difference in the principle and there should be none in the practice."