The former West Lothian MP said he believed the SNP’s new group of MPs would “settle down and do an honest job” in the House of Commons rather than agitate for independence.
But he has admitted Scottish independence would be a possibility if Britain votes to leave the European Union.
The former father of the Commons also accused of David Cameron of “disgraceful” and “truculent” behaviour by calling for the introduction of English votes for English laws within hours of the independence vote.
However, speaking at the Edinburgh International Book Festival, Mr Dalyell insisted many of those who voted for the SNP in May were merely disillusioned with the Labour Party.
Dalyell, a long-time opponent of a Scottish Parliament, said Labour had made a fatal mistake by promising more powers for Holyrood and said the devolution process had set many Scots “travelling on a road on which they never intended.”
He said he feared there would eventually come to a point when Scotland would be “indistinguishable from a separate state” if MSPs were given more and more responsibility.
Asked by broadcaster James Naughtie whether he thought independence was “inevitable”, Dalyell said: “No, 55 per cent of the people of Scotland don’t want it. The majority have rights.”
He added: “I think good sense will prevail. I don’t think there will be another referendum for a generation, that’s what was promised, for 10 years. I hope the SNP contingent will settle down to doing an honest job in the House of Commons.
“As time goes on, I think you may find that the SNP group in the House of Commons will become less enchanted with directions from Edinburgh.”
Asked where Scottish Labour had gone wrong in the recent General Election campaign, he said: “What I think was missing was they should have been quite clear that if more powers were to be given to the Scottish Parliament it would come to a point where that would be a break-up of the United Kingdom - 55 per cent of people don’t want that.
“Many who voted for the SNP in the election did so because they were dissatisfied with Labour. But equally they weren’t going to want the severing of ties with the rest of Britain. I don’t think powers for the Scottish Parliament were uppermost in the minds of people.”
Meanwhile Mr Dalyell said Jeremy Corbyn, the front-runner in the Labour leadership contest, should be “given a chance” to lead the party,
He added: “He is certainly a possible alternative Prime Minister. He could quite clearly bring a whole lot of young people to the party.”
Mr Dalyell said it would be “absolutely ludicrous” for any new Labour members to be excluded from voting in the contest if they had previously spoken out against the party.”