Rachel Reeves accused the SNP of a “real lack of understanding about how on earth people are going to get through the next few months”.
Councils across Scotland have been hit by bin strikes, with hundreds of schools and nurseries also set to close for three days next week when staff walk out.
Trade union leaders have rejected an improved pay offer from Cosla, the local authority body.
Ms Sturgeon previously said the Scottish Government had “exhausted all options” to make more funding available, insisting its budget is “finite”.
Ms Reeves accused the SNP of wasting money on “various failed schemes”.
She was asked about the strikes during a visit to Catapult, a leading innovation and research centre for offshore renewable energy, in Levenmouth, Fife.
The shadow chancellor said: "It's the first thing you notice when I got off the train at Waverley.
“You see it as you go all around the city, and it is really sad during the festival, for this to be what people’s experience is.
"I do think that Nicola Sturgeon and the SNP sound quite tin-eared to the concerns of low-paid public service workers, who are genuinely really worried about how they are going to pay their bills this autumn and winter.
"From what I've seen, the proposal that has been put forward is sort of 'take it or leave it' and it does sort of sound like a real lack of understanding about how on earth people are going to get through the next few months.
"And that's why the Scottish Government do need to be using all the powers they've got to help people through these winter months.
"Instead of wasting money on various failed schemes, actually get the money to the people who most need it."
Ian Murray, Labour’s shadow Scottish secretary and the MP for Edinburgh South, accused the Scottish Government of absolving itself of any responsibility.
He said: "They spent the first ten days of the strike blaming Edinburgh Council for the bin strikes, when in actual fact it's a Scottish Government pay rate that has to be set and the Scottish Government need to fund it.
"So rather than pointing fingers, they need to be sorting it out.”
Mr Murray said the rubbish at Bute House, the First Minister’s official residence in Edinburgh, is collected by a private contractor, “which in itself shows you the problem of Scottish politics at the moment”.
Elsewhere, Ms Reeves said her party’s proposals to immediately freeze the energy price cap would save Scottish families £2.6 billion.
A major clean-up operation has been taking place in Edinburgh as waste and cleansing services resumed after nearly two weeks of strike action.
Workers are set to walk out again next week, with Unite industrial officer Wendy Dunsmore warning that a “winter of discontent” lies ahead.
She told the BBC: “We are absolutely resolute that this is going to be a winter of discontent and it will escalate, but we are hoping against all hope that the Scottish Government and Cosla will see sense and get back round the table with a proper rise for the lowest paid within local authorities.”