None of the party’s 111 candidates won a seat in the local elections in Scotland.
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 none of the candidates managed to gain a seat in any of Scotland’s 32 local authorities, the same fate that befell the party at last year’s Holyrood election.
Among those to lose their seat was Chris McEleny, the party’s general secretary.
Speaking on Friday, Mr Salmond said: “Our 111 candidates fought a fine campaign and our vote registered everywhere.
“In a number of wards the Alba vote came in at over 5%, but the instruction from the SNP leadership not to use preferences to support other independence candidates now condemns most Scottish councils to control by unionists.
“However the awareness of Alba is much, much greater than previously. We found people friendly and receptive to the Alba message but still to be convinced about the vote.
“Alba is undaunted and will continue to press hard on the urgency of independence.
“It was Alba pressure which brought discussion on the timing of an independence ballot to the fore in this election.
“In the event of the promised referendum next year, our party will unite with others behind the Yes campaign.
“If, however, it does not take place then, the SNP will reap the electoral whirlwind in coming elections.
“Alba is also focused primarily on the tactic of maximising the pro-independence votes at Holyrood and the next Holyrood poll is our number one target.”