Guests invited to the tenth anniversary celebrations of the museum were told that it was important that the money should be raised in the next six months to cover costs while an action plan for the future was put in place.
Vicky Bagnall, chairman of trustees, told guests that the coming year was likely to be "among the most difficult".
She said: "The continuation of starts and stops with the Covid-19 pandemic and despite support from national and local government, crowd-funding and donations we survived the first lockdown and were in a good situation.
"However, many of our volunteers were classed as vulnerable people and we had to bring in staff to fill those places.
"Over the last two years people have been nervous to come out into closed environments.
"School visits have picked up but group visits have also fallen.
"We are £20,000-a-year short to pay these extra staff and earlier this year our gas bill went from £4,000 to £16,000-a-year.
"We are grateful for government support but other costs have also risen.
"There is the expectation of another fall-off in visitor numbers as the cost of living increases and starts to impact.
"We do have two trump cards with our tenants, Forte Cloth and the National Carpet Cleaning Association, who share our passion for carpets and design.
"We hope the Cleaning Association will bring their members to become our members, linking to show the future of carpets and design."
She said that the museum had "an extensive archive" and that there were ways of licensing the designs through which it was hoped the museum would generate money.
Vicky said that it might take twelve to eighteen months before the project generated income and that meanwhile it was hoped the appeal would bring in £15,000 in the next six months through donations and fundraising activities.