Mr Smith, who has the support of Scottish Labour leader Kezia Dugdale to replace Jeremy Corbyn, said Labour has “too often looked far too London-centric”.
The Welsh MP said his experience living in a devolved nation gives him insights into what Labour needs to do to win back support in Scotland.
Mr Smith is often described as a “Blairite” but he said his leadership style would be more like Tony Blair’s predecessor John Smith - the Scottish MP who died while serving as leader of the opposition in 1994.
In a webchat on the Mumsnet website, Mr Smith was asked what he would do to give Labour a chance of winning seats in Scotland.
He said: “On Scotland, I think my experience as a Welsh MP in a devolved era gives me insights into what we need to do to win back support.
“First we need to show that Labour understands the importance people attach in Scotland to their patriotism and their identity and to allow the Scottish party and the Scottish people to determine their own destiny.
“Too often we looked far too London-centric.
“Secondly, we need to invest in Scotland, and I would through my £200 billion British New Deal.”
Asked if his style of leadership would be more like Mr Blair or John Smith, he said: “Definitely more like John Smith, one of my great heroes, and a tragic loss to the Labour movement.”
Ms Dugdale has pledged to “consider all options” to protect Scotland’s relationship with the European Union.
However, she stressed that the Scottish Labour manifesto in 2016 ruled out another independence referendum in the lifetime of the current Scottish Parliament and “we won’t be changing our minds any time soon”.