Fine Gael Director of Elections Brian Hayes has said the party "underestimated the unpopularity of the Government" going into the election".
Mr Hayes said he "accepted responsibility" for what happened and the parliamentary party now needed to assess what happened in the election.
Speaking on RTÉ's Today with Sean O'Rourke, he agreed there is a "degree of truth" in the assessment that the Fine Gael campaign was too Dublin-based.
He said it had to be asked why "the undecided voters had gone against the outgoing government".
Mr Hayes argued that: "Government is a very difficult place to be when you are increasing taxes and cutting services."
He said now was not the right time to scapegoat Taoiseach Enda Kenny and "time is now needed to reflect on how the next government will be formed".
He said he was still confident that "Irish democracy was strong".
Mr Hayes said it was time to move to a "new space" and this would require all TDs to play a big role in legislation and "take parliament seriously".
Mr Hayes said this would be a good departure from the "punch and judy" politics that currently existed.
Speaking on the same programme, Fianna Fáil Spokesperson on Environment & Local Government Barry Cowen said the Dáil and its members have to "look at the message that has been given to it by the electorate".
He said it is "incumbent on those who have been given the responsibility to now make the Dáil more relevant".
Mr Cowen said the people have asked for a more meaningful and relevant Dáil.
He added that Irish Water was a prime example of something "pushed through without meaningful debate" and repeated that abolishing Irish Water remained a "top priority for Fianna Fáil".
Mr Cowen said that Fianna Fáil would meet tomorrow to allow all members, new and existing, to debate all the issues.
Meanwhile, Sinn Féin Leader Gerry Adams has said his party is in discussions with various independents and smaller parties in relation to the formation of the next Government.
He made the comment at a media doorstep in which he called for a "Commission of Investigation" to be set up to examine new allegations regarding the purchase of Northern Ireland's property portfolio.
A number of politicians have entered Government Buildings this morning ahead of a Cabinet meeting, including Taoiseach Enda Kenny and Tánaiste Joan Burton.
Listen to Brian Hayes and Barry Cowen on Today with Sean O'Rourke:
Disconnect between Govt and electorate - Phelan
Fine Gael TD John Paul Phelan has said that Enda Kenny took over the country when it was "in a mess" five years ago and not even his harshest critics could deny it is "in a better place now".
The Carlow-Kilkenny TD said the parliamentary party meeting on Thursday will be the "opportunity to discuss all matters surrounding the election in a clear and frank manner", including the leadership of the party.
Mr Phelan added that there was a disconnect from a part of the electorate and some of those in advisory roles during the campaign.