The pro-independence party, which launched at the start of the Holyrood campaign, had been fighting on the regional list section of the ballot, with the declared aim of winning an independence “supermajority”.
But while list votes are still be counted, he said his new party looked set to fall short of the amount needed to pick up seats.
Mr Salmond also claimed that there could be “perhaps even a million list voters” for Nicola Sturgeon’s party which would “elect nobody”, because of the SNP’s success in the constituency section of the vote.
Speaking to the PA Scotland news agency, Mr Salmond said: “We warned of the danger of piling up SNP list votes and achieving nothing, getting nobody returned and allowing unionists, Labour and Tory, to sneak in the back door. That unfortunately is what is going to happen.”
Mr Salmond, a former SNP leader, said supporters of the pro-UK parties had been “smart” in tactical voting but that “the SNP unfortunately are sending their troops over the top and are piling up perhaps even a million list votes, which will elect nobody”.
Speaking about the votes Alba has received, he said: “I’ve obviously looked at the ballot boxes at the count and they’ve given us some very good ones – Aberdeenshire had over 10% in a couple of the ballot boxes.
“But in some of the big ballot boxes, I think we ended up over 3% in Aberdeenshire East, the same in Banff and Buchan, a bit more actually, which I’m pleased with because these are our best results in Scotland.
“But that doesn’t get you a seat. You need 4.5%, maybe 5%, to get a seat. But nonetheless it’s a credible performance for a party which has just celebrated its sixth birthday – in other words, we are six weeks old.”
The former first minister insisted: “I think Alba’s future is secure.”
He congratulated Ms Sturgeon, his successor as SNP leader, “on her victory” in the election, but added that that came with responsibilities.
Mr Salmond said: “It is now Nicola’s responsibility to carry forward the independence argument and she now has to answer the questions of how you proceed with obduracy from Westminster.
“Now I think Alba brought forward a number of ways to do it and we pointed the way. I wish Nicola luck in getting that forward, and Alba will be there urging things on.
“And I suspect the existence of Alba will be an additional incentive for those who have gained election to the Scottish Parliament to get on with the job of delivering the Scottish people independence.”
The former first minister added: “I know that the SNP have been a little bit nervous, sending people letters saying if they are associated with Alba they might be disciplined by the SNP, or all sorts of things.
“But I put that down to over-enthusiasm of some people who just joined the SNP and are perhaps not aware of the politeness with which the SNP normally conducts its operations.”