Minister for Children Norma Foley has said she was surprised that Michael Healy-Rae resigned from his position as a Minister of State over the Government's response to the fuel crisis.
Yesterday, Mr Healy-Rae announced his resignation in the Dáil chamber and voted against the Government's motion of confidence.
Mr Healy-Rae said that he could not, in his heart, vote confidence in the Government.
However, the Coalition won the confidence motion by 92 votes to 78.
Watch: People in Healy-Rae's heartland in Kilgarvan asked if he was right to resign
Speaking on RTÉ's Morning Ireland, Ms Foley said the Government never likes to see anyone walk away, but it came through the vote and "still has the majority".
"The Dáil last night endorsed that leadership, that Government, and we've a job of work to do and we don't walk away when things get difficult, so we'll do the job of work," she said.
Ms Foley added: "Twenty-four hours earlier, Michael did put out a video where he had said he endorses the package.
"He believes it was a very good deal for the people of Ireland, something for everyone, that he would be voting confidence in the Government.
"So, I am surprised that he did what he did. But Michael has to do, and indeed any [TD] has to do, what they have to do.
"But Government has to lead, and Government in times of international turmoil has to provide steady leadership.
"That has been endorsed last night and the Government will go about the body of work that needs to be done."
Speaking yesterday, Mr Healy-Rae said the sight of grown men crying over the cost of fuel left him with no choice but to leave the Government.
"Because of the fact that I believe this Government have let the people of Ireland down, I will be voting no confidence in the leader of the country, and I will be tendering my resignation as Minister of State from now," he said.
"The people of Kerry are telling me, they are unhappy with this Government. They don't want to see me or any Healy-Rae supporting it," he said.
Watch: The moment Michael Healy-Rae tells the Dáil he will resign as Minister of State
Ms Foley said she was not aware that Mr Healy-Rae was not going to support the Government and, as far as she knew, no one in the Coalition was aware that he was going to resign.
Mr Healy-Rae's brother, Danny, also voted against the Government.
"There was an arrangement made with the Healy-Raes that would mean that two of them would support Government for the lifetime of Government. That didn't materialise yesterday," Ms Foley said.
She added: "I think the world knows that when the arrangement was made with both Healy-Raes, it was a matter for two Healy-Raes to support Government.
"I regret to see them walking away, but that's a matter for themselves."
Ms Foley said the Government is "standing up ... delivered yesterday, cumulatively, a package of over €750m to support the economy".
"You have to manage what you can, you have to cut your cloth to suit the measure at a given time, keeping your eye to the future, mindful that there may well be further shocks," she added.
Sinn Féin Spokesperson on Justice Matt Carthy claimed the Government had shown arrogance towards ordinary people and had lost the confidence of the Irish people over its handling of the fuel cost protests.
Speaking on the same programme, Mr Carthy added that the Government surviving the confidence vote represented a "bad day for people all over the country".
He said the Coalition acted over rising fuel costs "only when significant pressure was exerted" on it and then acted "in half measures".
He said the Government is weaker despite winning the confidence vote after losing the support of the Healy-Rae TDs.
"This Government is running out of road, despite the numbers in terms of the votes last night," Mr Carthy said.
His party colleague David Cullinane said the Government surviving the confidence vote "isn't about me or Sinn Féin, that's for sure, it's about the people who took to the streets, ordinary people who are to the pin of their collar".
Speaking on RTÉ's Today the David McCullagh, the Spokesperson on Health accused both the Taoiseach and the Tánisate of "arrogance" in recent weeks that he said not only "hurt" the Government but "angered" people, "created real frustrations, exacerbated the situation that should never have come about in the first place".
'Didn't expect that' - Harkin
Minister of State Marian Harkin said she did not expect her colleague in Government Michael Healy-Rae to resign yesterday and was sorry to see him go.
Speaking on RTÉ's News at One, the minister said Mr Healy-Rae's resignation "seemed to be a surprise to everyone".
"I just didn't expect that what happened - did happen," she said, adding: "I'll have to leave Michael to explain all of that himself."
Ms Harkin said that two days previously, Danny Healy-Rae "had spoken about the need for both of the leaders of Fianna Fáil and Fine Gael to be changed in quite trenchant terms".
"Danny and Michael came together as a package, as it were," she said.
Ms Harkin added: "When we negotiated the Programme for Government - I was one of the three negotiators - we negotiated on behalf of the Regional Independents, we knew that Danny and Michael were talking to the Taoiseach and the Tánaiste.
"When our deal was struck ... I think it was Danny who said they were 'the fourth leg of the stool'.
"So, their arrangement was completely separate to ours."
'Huge pressure' on Healy-Rae to not support Government
Mr Healy-Rae was under "huge pressure" from his supporters to not back the Government in a confidence motion over its handling of fuel cost protests, according to an Independent councillor in Co Kerry.
Cllr Niall 'Botty' O'Callaghan said Mr Healy-Rae's decision to leave Government is "going down with mixed feelings" in Kerry.
"His supporters wanted him to step away, and the pressure was there for him to step away, and I understand why he did it.
"But there's also the side of the argument, are you better off at the top table and being able to influence things, because if something happens down the road, let's say three or four months' time, and we have the same issues that we had last weekend, he's not going to be at the top table, he's not going to be there to speak," he said.
Mr O'Callaghan added that from his perspective Kerry is worse off now with Michael Healy-Rae out of Government.
"The Government are going nowhere. The Government had the numbers. So, I think people need to calm down a little bit and understand that this Government were elected and it was a democratic election," he said.
Social Democrats TD Gary Gannon said there is a "huge amount of hurt out there" among people "comparable" with the austerity years following the financial crash.
The Dublin Central TD added that as an "on the ground" politician, Mr Healy-Rae would be feeling "that very same message" from his constituents.
Mr Gannon said that the Opposition is "stronger this morning" after "taking the voices of the people that elected us" back to Dáil Éireann.
