Opposition politicians say Labour's defeat in the two Blaenau Gwent by-elections is "hugely damaging".
Nick Bourne, Conservative leader in the Welsh assembly, said the results changed the face of Welsh politics.
Plaid Cymru MP Adam Price said Labour's losses in both assembly and Westminster seats had "historical significance".
But First Minister Rhodri Morgan said the switch to the independents was to a "dustbin for the disaffected" and the valleys needed "progress not protest".
Independent candidates Trish Law and Dai Davies became the AM and MP respectively in a seat which used to be a loyal Labour constituency.
Mr Bourne said the result indicated that the Labour party was "finished in Wales."
"They cannot take any community for granted," he said.
"Tribal loyalties have broken down, people have looked at the manifestos of the different parties, they have said we don't want Labour in a community which used to be rock solid for them.
"They have lost in their heartland."
Mrs Law inherited the assembly seat from her husband Peter, who died in April. He had been the Labour AM, but left the party in protest at an all-women shortlist to select the parliamentary candidate, stood as an independent and became the MP as well.
Mr Price, MP for Carmarthen East and Dinefwr, said that to lose three times in just over a year was of "huge historical significance".
Owen Smith lost by nearly 2,500 votes
"I never thought I would see the day the Labour Party would lose once in Blaenau Gwent, but to lose three times in just over a year is hugely significant."
He said that Labour had tried to present itself as "old" Labour with the visit to the constituency of Chancellor Gordon Brown.
'On its last legs'
"This is just as damaging to Gordon Brown as it is to Tony Blair because it was about the popularity of the Labour Party as a whole.
"(Labour candidate) Owen Smith has presented himself as a Brownite, not a Blairite and he has still lost Blaenau Gwent.
"This is hugely damaging to the Labour Party because there are no safe seats left in south Wales."
Liberal Democrat Dewi Knight said: "We will be celebrating the fact that this failing (assembly government) administration is on its last legs and Rhodri Morgan will not be first minister for much longer".
Defeated labour assembly candidate John Hopkins was greeted with some heckling when he said in his speech after the result that he was "very pleased with the swing back to Labour".
He said: "For the mathematicians among you - you may want to be cynical - but we started off with a deficit of over 9,000 (votes).
"And if you look at the figures you will see what I am talking about."
Mr Hopkins said Blaenau Gwent needed jobs and attracting them would be a difficult task for any candidate.
"As a Labour politician I'll be keeping my eyes very clearly on the successful candidates."
First Minister Rhodri Morgan said it had been a protest vote "because somehow or other faith in politicians and parties seems to be a bit low at the moment".
"I look back at by-elections of the past where normally you'd get a classic switch from Labour to Conservative, Conservative to Labour and back in the late 80s.
"But now you're getting a switch from the party of government to independents or the Liberal Democrats as a sort of party of protest, a dustbin for the disaffected if you like."
He added: "In a way what the valleys need is progress, not protest."
Labour party chairman Hazel Blears said: "Over the last year, we've been working very hard but clearly it wasn't long enough to bring the seats back.
"We actually reduced the independent majority dramatically but clearly there are issues here for us and we're listening, taking that seriously"
"We had very good candidates and given a longer period of time, we would have done even better than we did last night."