The First Minister made the concession at a referendum event last night, but Labour hit back, saying it does not go far enough.
Mr Salmond said he admired "certain aspects" of the controversial politician's leadership in an interview published in GQ magazine amid the escalating crisis in Ukraine and Russia's annexation of Crimea.
His comments to interviewer Alistair Campbell, the former Downing Street spin doctor, were made after the Sochi Winter Olympics.
They caused upset among the Ukrainian community and provoked criticism from political rivals.
Mr Salmond was asked whether he regretted the comments during a question-and-answer session at the event in Dundee last night.
An audience member asked him what the topic of conversation would be were he to be stuck in a lift with Better Together leader Alistair Darling, the Prince of Wales and Mr Putin.
"The topic of conversation most certainly would be how to conduct interviews without getting your foot stuck in your mouth," Mr Salmond said.
Asked about the GQ interview, he said: "I regret the way it was characterised. I defended the remarks I made in the parliament.
"I suppose maybe I should have had the wit to realise that Alastair Campbell doing an interview for GQ … was probably an occasion where I should have been more careful with my language.
"Prince Charles and I know well that you have to be careful with comments."
Patricia Ferguson, Scottish Labour's external affairs spokeswomen, said the "half-hearted apology doesn't begin to address the offence and embarrassment Alex Salmond caused Scotland with his comments about Putin".
She added: "Rather than blame everyone else for this outrageous blunder, Alex Salmond should just say sorry.
"Anything else will leave lasting damage to his reputation and, sadly, Scotland's."