A Green Party TD said they ran a good campaign in the referendums on Family and Care.
Junior Minister Joe O'Brien said the count is not over and that it is 'early days'.
He said there would be no formal decisions made at this stage around the result.
Minister Eamon Ryan earlier appeared to admit defeat on the two constitutional questions, suggesting the case put to the public 'didn't win'.
Voting began with a slow start yesterday, with turnout results projected to be mixed across the country by the time the polls closed at 10pm.
Early indications suggested a loss for the Government on both questions.
Counting in the Family and Care Referendums at Dublin's RDS, 9-3-24. Image: Leah Farrell/© RollingNews.ieMinister O'Brien told Newstalk the count is only beginning.
"I think it's early days, we're in one count centre here we've got many across the country," he said.
"Certainly indications here at the moment are not good but we don't want to be making any kind of formal decisions or commitments at this stage.
"I think it was a successful referendum ultimately in terms of turnout, turnout was a bit better than I think a lot of us were expecting initially.
"It's the first electoral event we've had in four years since COVID as well; I think it's really good to see people exercise their democratic right".
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Minister O'Brien said he believes the media was the main battleground.
"I think this campaign was very much fought in media - broadcast media, print media and social media," he said.
"What we found when we hit the doors was that we were able to explain to people in more detail and to bring them over to the Yes side as well.
"I think in hindsight it would have been good to see more people knocking on doors".
He added that he believes Government parties "all did as best we could".
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