The former first minister of Scotland was speaking at an Alba campaign event in the Scottish capital despite opposing parties suspending their operations out of respect for Philip’s passing.
It comes amid disappointing polls for his new political project which suggest support is lacking ahead of the Holyrood elections in May.
He said: “The Duke of Edinburgh – it won’t surprise anyone to know – was not one of the foremost advocates of Scottish independence I’ve ever met.
“But I found the disagreements enjoyable, he did as well.
“To me, at least, he seemed to enjoy nothing more than a good argument – and a forthright argument.
“One thing I know absolutely, he was a get-on-with-life sort of person – get on with it, no maudlin sentimentality.
“An extended mourning in the country would not have been to his liking, I can be absolutely certain about that.
“He would have wanted folk to get on with their lives, recognise and pay respects for a hugely long-standing public service.
“For the rest of us, his message would be absolutely, ‘get on with it’.”
A survey of 1,007 over-16s in Scotland suggests an SNP majority or an SNP/Green coalition would have the most backing as the “best mandate” for a second independence referendum, rather than involvement from Mr Salmond’s new party.
Results of an opinion poll, carried out for The Scotsman newspaper by Savanta ComRes, published last week suggested the SNP would win 64 seats and narrowly miss out on an outright majority.
It predicted 10 pro-independence Scottish Green MSPs would be elected but Alba, on 3% of the regional list vote, would fail to gain any seats.
But Mr Salmond claims almost half of SNP voters get on board with the idea of creating a supermajority in the Scottish Parliament by giving their regional list vote to Alba.
He added: “It will fundamentally change the power balance between Scotland and Westminster and propel us on the road to independence.”