Independent TD Mr Harry Blaney said the Government had "no one to blame but themselves" for the defeat of the amendment. His Donegal North East constituency recorded the highest Yes vote in the State and he said he believed this was partly due to work done by his supporters.
Mr Blaney, who said the holding of a referendum was part of the agreement he had with the Government "from the first day", accused Fianna Fáil of failing to promote it on the ground.
"I don't know if their hearts were in it at all or not. Certainly there are some Fianna Fáil people who had their hearts in it, but not all of them, and I don't know about the people at the top," Mr Blaney said.
He said the first mistake the Government had made was in splitting the anti-abortion vote by protecting the life of the unborn only from implantation.
He conceded that he and the other Independents could also be partly to blame for allowing such a wording to be put.
Ms Mildred Fox, the Independent Wicklow TD, said she was disappointed with the result but it was how the people voted and she accepted and respected that.
She said it was up to the next Government to decide the next step. "It would be very difficult for me to support the principle of legislating to provide for abortion," she said, adding that she would, however, look at whatever proposals were put forward.
Ms Fox said she would not be supporting any call for a further referendum on the issue.
Independent TD Mr Jackie Healy-Rae called for the setting up of a national forum to determine the views of the public on abortion once and for all. Mr Healy-Rae said the electorate was "none the wiser" after this week's referendum. "It was a very big exercise to achieve nothing," he told The Irish Times.
He added the Taoiseach would face problems trying to figure out what to do next. The South Kerry TD, who voted Yes but did not canvass support for it, said he had warned it was badly timed and could be defeated as a result.
The Taoiseach should not attempt to tackle the issue again until after the general election, he said. Even then, presuming Fianna Fáil was returned to office, there should be no rush.