A Welsh Assembly Government minister says a "sympathy vote" was behind Trish Law's win in her late husband's seat.
Trish Law followed her late husband Peter as AM for Blaenau Gwent
Environment Minister Carwyn Jones said her Blaenau Gwent by-election victory was not due to her policies as she had not highlighted what they would be.
Mrs Law became the AM for the area which her husband had served both at the Welsh assembly and Westminster.
John Mason, for Mrs Law, said there may have been sympathy, but voters thought Labour was taking them for granted.
Mr Jones said Mrs Law's win on Thursday was due purely to a sympathy vote after the death of her husband Peter in April.
Mr Law left Labour in protest last year over the party's use of all-women shortlists to pick its parliamentary candidate.
He stood for Westminster as an independent at the general election, and became the area's MP, as well as representing it in the assembly.
But he died within a year after developing a brain tumour.
His widow became the independent AM with a majority of more than 4,400. His former agent, Dai Davies, was elected independent MP with a near-2,500 majority in a seat where Labour used to hold a 19,000 majority.
Mr Jones told BBC Wales' Maniffesto programme that the results were not a sign of a new development in Welsh politics, and history showed that by-election results were overturned in general elections.
Carwyn Jones says Labour will review the Blaenau Gwent results
But he said that the Labour Party would review the results and listen.
Impact on policy
Mr Mason, publicity agent for Mrs Law, said: "There may have been an element of sympathy. But the results show, by walking through the streets and talking to the people of Blaenau Gwent, that Labour said they would sort out its policies.
"The people of Blaenau Gwent believe Labour had started taking people for granted. Where policies are concerned, an independent voice in the assembly will have an impact on the policy-making decisions there."
Mr Mason said another Labour AM would "just merge back into the political system".
He said the Blaenau Gwent People's Voice group - which backed the independents - did not see these results as a "blip".
"Various circumstances could occur in next year's assembly elections where Labour could lose more seats," he said.
The results also led to claims that Prime Minister Tony Blair could leave office more quickly, but UK Culture Secretary Tessa Jowell called for an end to the speculation.
She told BBC1's Sunday AM programme that the by-election results in Blaenau Gwent and Bromley and Chislehurst were "bad", but added: "At this point mid-term by-elections are unlikely ever to be good for the government.
"We have pulled back from the general election but every single by-election defeat like this sends a message we have got to listen to."
Ms Jowell continued: "I know everybody in SW1, in the Westminster village, is talking about this. I'm afraid they talk about little else.
"But I think as a government, if we are not going to squander a third term, let's just turn out from Westminster and talk to the people of this country.
"That's the message of Blaenau Gwent," she said.