Advocacy group Care Champions said the move is a “missed opportunity for answers and reform”.
Group spokesperson Majella Beattie said: “The Government’s proposed evaluation of the Covid-19 pandemic response is a cynical attempt to evade scrutiny and silence the voices of the bereaved.”
She spoke out after Taoiseach Simon Harris defended the decision to “evaluate” how the Government handled the pandemic.
He said an evaluation process will “get to the bottom” of Ireland’s response to the pandemic in a timely way.
Mr Harris, who was the health minister for the first four months of the pandemic, said authorities got a lot of things right, but also that people experienced a lot of hurt during the health emergency.
Tánaiste Micheál Martin said he was looking forward to sharing his reflections of being taoiseach during that period, adding that he had “no doubt” senior public health figures will voluntarily take part in the probe.
Ms Beattie said the evaluation was “inadequate” to meet the standards of a “credible inquiry”.
She added: “We will continue to fight for a genuine inquiry that delivers justice and brings an opportunity to truly reform the care sector.
“The inquiry must also provide a safe and supportive environment for patients, residents’ families and healthcare workers to share their experiences.”
The move to set up an evaluation has been criticised by opposition TDs for not having the power to compel witnesses.
Aontú leader Peadar Tóibín said the evaluation was “wishy-washy” and called for a full public inquiry, while People Before Profit-Solidarity TD Mick Barry said it was “toothless”.
Anne Scott, a professor emerita with University of Galway whose research interests include the ethics of healthcare, is to lead the evaluation of how the country managed Covid-19.
Meanwhile, PA Duffy and Co Solicitors, a firm representing over 50 families, said the proposed evaluation would fail to provide families with answers.
“The bereaved families who I represent feel betrayed by the failure to establish a statutory inquiry,” Enda McGarrity, a solicitor at the firm, said.
“Our clients have long held the view that a non-statutory investigation without the powers to compel witnesses and evidence would not be fit for purpose as it would be incapable of fully establishing the facts of what happened.
“This is particularly true in respect of care homes, 80pc of which are run by private entities which would have no legal obligation to provide evidence to a non-statutory evaluation.
“The Government did not consult with bereaved families on the terms of reference despite numerous attempts by our clients to engage in discussions.
“Our clients believe it is not possible to learn lessons for a future crisis without placing the interests of those who suffered most at the centre of any inquiry.
“They consider that the Government have failed to deliver a mechanism capable of giving them the answers they deserve.”