Ms Sturgeon told an audience in Rutherglen how the crisis has grown, with demand soaring in recent years.
Earlier, First Minister, Alex Salmond, said the growth of food banks and increasing inequality was one reason why he believed Scotland must be independent.
The Scottish Cabinet met in Rutherglen and then held a public question and answer session with local people in Fernhill Community Centre.
Ms Sturgeon said: "People who run food banks deserve our gratitude and thanks.
"There will always be the need for support, but that should be through the state welfare system.
"We are seeing an explosion in demand for food banks as a result of the UK government policies.
"There are three food banks within a mile of this centre. Demand for one in Govanhill in my constituency is such that for the first time I now hold vouchers in my constituency office because of people coming in who are in need."
"I want to live in a country that doesn't have so many people dependent on food aid."
Mr Salmond said: "In 2001 the Trussell Trust operated one food bank - now it has 43."
He said they were not only in poorer areas but he had visited one in an affluent town in his own constituency.
He also said the growth in demand for food help was down to policies coming from Westminster which Scots were powerless to stop.
He said: "For more than half my life Scotland has voted in one direction and the rest of the UK another and we got a government we didn't vote for.
"If you allow that to continue then the growth of food banks and iniquitous policies like the bedroom tax will continue as well."
Mr Salmond and his cabinet ministers answered questions on nuclear weapons, currency in an independent country, pensions, housing and international drug dealing.
He held his weekly cabinet meeting in the community centre before the public meeting in front of around 150 people.
He said there would be no negotiating on removing Trident with the UK Government, and said the nuclear submarines would be moved within the first four years of an independent Scotland.