The Scotsman (p4) reports that the rebuke was delivered by members of the parliament's housing committee, as they gave their backing to the executive's proposals.
Ms Alexander is the force behind the biggest housing transfer scheme in Europe, which, if it goes ahead, will see 150,000 homes passed to housing association landlords.
The discussions about the executive's plans for council-owned housing led to the first major fall-out between MSPs on parliament's influential cross-party committees.
The three Scottish National Party members claimed there was a possibility that stock transfers could lead to privatisation by the back door and called for the Scottish executive to consider other options for the badly needed financing of council housing.
Ms Alexander is pursuing the stock-transfer policy in the belief it will ensure all of Scotland's 'socially rented' homes will be warm and free of damp within ten years. The plan is also designed to wipe out council debts, which run into millions of pounds across Scotland.
Some tenants groups claim the plans will inevitably lead to high rents and job losses among council workers.
Despite the conflict between housing committee members, the MSPs joined forces yesterday to issue their consultation ultimatum to Ms Alexander. Mrs Curran, while cautiously welcoming the executive's proposals, criticised the housing minister for failing to involve tenants properly in the process.
She said: 'We would say to the executive: If you want to make this work, you must involve tenants in the process. They did not find ways of trying to include tenants. The principle of tenant involvementand transparency should have been much more critical to the process.'
Robert Brown, a Liberal Democrat member of the committee, said: 'Tenants did not have ownership of the process, and that has caused fear, apathy and resentment.'
However, Ms Alexander insisted yesterday that tenants were at the heart of the proposals and said£1m was available to fund the consultation process.
The housing committee's report is generally supportive of the executive's plans. However, a minority of MSPs - all SNP - raised concerns that the proposals could lead to privatisation of council housing stock.
In their report, the majority members of the committee agree major additional resources are needed to bring council housing - 93 per cent of which fail government standards of heat insulation - up to scratch.
They back the principle of stock transfer as the primary means of this cash being accessed, as well as providing effective community ownership of housing, but reject the idea this amounts to privatisation.
However, the report calls for the executive to examine alternatives, should the tenants reject stock transfer, and make public its examination of the other ways in which finance can be secured.