Lord Reid said the reality of a Yes vote next month would be billions of pounds of cuts to public spending.
He went on to warn that if an independent Scotland was forced to use the pound without a currency union being agreed, the impact on services such as schools and hospitals could be "devastating".
Lord Reid, who also served as home secretary and defence secretary in Tony Blair's government, hit out at Scottish First Minister Alex Salmond, claiming he "speaks with the confidence of a man blinded by his own ambitions".
Lord Reid said: "We got rid of the divine right of kings several centuries ago - we're not about to replace it with the divine right of the first minister."
Lord Reid, who was speaking at Dalkeith Miners' Club in Midlothian, argued: "Far from offering a vision of a socially just Scotland, the reality is that an independent Scotland would risk cuts to public services worse than anything imposed by Mrs Thatcher.
"The experts at the impartial Institute for Fiscal Studies have said a separate Scotland would face spending cuts worth £6 billion in the first few years after independence.
" It doesn't take an expert to work out what that means for public services in Scotland."
But former Scottish Labour Party chairman Bob Thomson, who is now a leading member of Labour for Independence, said: "I could not disagree more. An independent Scottish Parliament offers a much better way of making sure that the wealth of Scotland works for all the people of Scotland."
A spokesman for Scottish Health Secretary Alex Neil also hit back, saying: "Lord Reid is on the same side as Margaret Thatcher's party in the debate - and Labour are paying a very heavy price for that alliance with the Tories."