The party put up 111 candidates – a number of whom were elected as SNP councillors in 2017 before defecting to Mr Salmond’s party when it launched last year – but failing to have any councillors elected.
Mr Salmond said it was “very disappointing” that Brian Topping, the Alba candidate and veteran of North East politics, took just 274 votes in the Fraserburgh District.
Mr Topping was a SNP councillor in Fraserburgh for almost 38 years before defecting to Alba last year.
Mr Salmond said: “It was very disappointing. Brian was our best hope.
"He was fourth on the first preference, but then got squeezed out. It was still a good result for him, because he came so close."
The former first minister said: “We are making progress, but it takes time.”
When asked if he was likely to return a single councillor, Mr Salmond said: “Our results would have to be going very strong to get one.”
On why he had been unable to pull significant votes away from the SNP, Mr Salmond said “there was a lot of awareness of Alba that was not there”.
He added: “We have had some outstanding candidates, but it takes time. We have lots of new people. We are learning all the time.
“Essentially our next target is the Scottish elections in four years’ time.
"We have 3.1 per cent of the share in Aberdeenshire today and to get elected to Holyrood you need 4-5 per cent. Our share of the vote is encouraging. It’s cash in the bank for the future.”
He said it remained Alba’s priority to get “Scottish independence addressed as matter of urgency”.
Mr Salmond said: “We need to end this prevarication. If that doesn’t happen, we would have thought our position in four years’ time will be strong.
"We want to put that to the test. Scottish independence is where Alba will stand or fall. People will look to Alba to inject urgency into the system.”
In Banff and District, Alba came last with Mr Salmond’s long-term friend and former SNP colleague Iain Cameron, who has 55 years political experience, polling just 73 votes.
Over in Inverclyde, Chris McEleny, the general secretary of the party, returned just 126 votes.
Mr Topping, whose election loss brings to an end almost 40 years of service to local politics, said he was “devastated” that he would no longer be a councillor.
One of Scotland’s longest serving council members, Mr Topping is known to many as Mr Fraserburgh.
However, he said he had “absolutely no regrets” about switching to the Alba party last year.
Mr Topping said: “I wouldn’t change it in any way.
"We have some fantastic new policies, but we are new kids on the block. People often just vote for the person with the right colour of rosette.”