Holyrood needs "significant new powers" but Labour must also set out how it will use them to improve people's lives, shadow Scottish secretary Margaret Curran said.
The Labour MP said it is clear people support having a "strong Scottish Parliament", but also stressed that when agreement is reached on further devolution politicians must focus on how to use the new powers.
The Smith Commission, which was set up by the UK Government to consider further devolution in the wake of the referendum vote, is due to publish its initial report this week.
There has been speculation Holyrood could be handed complete control of income tax north of the border, new powers over welfare and the responsibility for running its own elections.
After 16 and 17-year-olds were given a vote in the referendum, this would pave the way for this age group to also be allowed to vote in Scottish Parliament elections.
Ms Curran said the vote on independence had changed politics in Scotland forever, saying that while it was "the first democratic expression of Scots' wish to remain inside the UK", it was also a "wake-up call to the whole political establishment that change had to come".
The vote for independence reached 45% in the referendum, with Glasgow one of four local authorities where there was majority support for leaving the UK.
Ms Curran wrote in the Herald that "so many people, many in Glasgow and the surrounding areas, felt that the UK wasn't working for them, and they thought the best option for change was through the exit door".
In the wake of that vote she embarked on a tour of the areas of Scotland with the highest Yes vote, saying talks with the public in these places had told her "people want a confident, positive Scottish Labour Party with plans to take Scotland forward".
Ms Curran added: "They want us to be better. One man told me that Labour was allowing the SNP to have 'too much possession of the ball' and we needed to fight harder for his vote. He was still weighing up how he'd vote next year and wanted to see that we have the hunger to win and to change the country."
She continued: "Second, people want a strong Scottish Parliament. This didn't surprise me - I campaigned for devolution in 1979 and in 1997, I was an MSP for 12 years and a member of the Scottish Government for five. I know why people want our Parliament - and our voice as a nation - strong within the UK.
"That's why we made the vow during the referendum campaign and why we're working with other parties - including the SNP - to deliver more powers for the Scottish Parliament through the Smith Commission.
"I want the conclusion of those discussions to be that the Scottish Parliament gets significant new powers. And as I've said before, whatever package the Smith Commission comes forward with must respect the decision of the Scottish people to remain inside the United Kingdom, and must ensure that Scotland isn't financially disadvantaged.
"Once we have agreement on further powers it's then time to start focussing on how we use them. That's the final thing that people have been telling me. They want the Scottish Labour Party to be saying clearly how we'll change people's lives.
"The new powers for the Scottish Parliament will help us achieve that in Scotland. Scottish solutions for Scottish problems, as (former first minister) Donald Dewar once put it.
"However, people want all their politicians - and both their governments - to be working together. Both the UK and Scottish governments have a role to play in getting the best deal for Scotland."
Ms Curran added: "People across Scotland still want a strong Scottish Labour Party. But they want us to be better. In a matter of weeks, we will have a new leader. Between then and the general election it will be our challenge to show the people of Scotland that the Labour Party is the party they need it to be."
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