The new Government Chief Whip and Minister of State, Dara Calleary, said he was disappointed not to get a senior ministerial position but has been assuaged by the massive support he has received over the last 24 hours.
He told RTÉ's 6.1 News that he is honoured to be sitting around the Cabinet table and will be a vocal member of Cabinet.
The Mayo TD - who is also deputy leader of Fianna Fáil - said he would make the most of the opportunity that is in front of him.
Deputy Calleary said there is anger and frustration from people in his constituency and that representation and geography are important.
He said he would use that anger to be a very vocal proponent for Mayo and the West of Ireland around the cabinet table.
As Chief Whip, Mr Calleary said he will be working with every Minister to deliver their elements of the Programme for Government which he said is an ambitious programme for the regions.
Earlier today, he admitted he had been hoping to lead a Government department, but had been offered the role of Chief Whip following a "very difficult conversation" with the Taoiseach on Saturday.
The Fianna Fáil TD said no other job was offered to him by Micheál Martin.
Speaking on Midwest Radio, Mr Calleary said he would be a voice for the west at Cabinet and would work 24/7 to return the support expressed for him by people in the region over the weekend.
He said he was aware of the anger felt by people about the absence of a senior minister in the west of Ireland.
Mr Calleary said he was angry himself over the weekend, but that now was the time to dust himself down and make the most of the position he had been allocated.
Taoiseach Micheál Martin has insisted that the Chief Whip position is a very important position within any cabinet. He said that the Government was one for the "entire country".
But Fianna Fáil members around Mayo have expressed their disappointment and frustration following the Cabinet announcement.
The chairman of the Ballina Fianna Fáil Comhairle Ceantar said there would be "no welcome whatsoever" for Mr Martin, if he were to visit the town as Taoiseach.
Also speaking on Midwest Radio, Matt Farrell said Mr Calleary had the ability and drive to serve as a government minister and should have been the first person appointed by the Taoiseach last Saturday.
Another party official, John Maxwell from Louisburgh, said he was furious at the way Mr Calleary had been treated.
He said that for the last number of years Mr Calleary had "Micheál Martin's back" when Fine Gael ministers were "wiping the floor with him".
He said the weakness of the party leader had led to the loss of a Dáil seat in Mayo last February.
He said it was now time for party members in the west to come together and get someone who would recognise the region to lead the party.
Mr Maxwell said he is "seriously considering" resigning his membership of the party as a result of Mr Calleary's exclusion.
The editor of the Western People newspaper said there was a real sense of anger and dismay in the region that - for the first time - there is "not a single minister" appointed from west of the river Shannon.
Speaking on RTÉ's News at One, James Laffey said it was "astonishing that it has been allowed to happen", both practically for the rural west and in terms of history given that the new Government will be in place to mark the centenary of Ireland's independence.
He said there was particular shock and disappointment that Mr Calleary has not been appointed to Cabinet and that many in Fine Gael locally were equally outraged by the decision.
Minister for Public Expenditure and Reform Michael McGrath said he met Mr Calleary this morning and he very much respects the open and honest way he has dealt with his appointment as Government Chief Whip.
Speaking on RTÉ's Today with Sarah McInerney, Mr McGrath said the Taoiseach and other party leaders faced difficult choices in selecting ministers. He said every constituency in the country will be represented at Cabinet.
Independent TD Mattie McGrath has criticised the lack of a Cabinet minister from the south-east or the western seaboard in the new Government, describing the omission as "devastating" for rural Ireland.
The Tipperary deputy said that when the group of Rural Independents recently met with the three party leaders who are now in Government, they were "assured" that their submissions and requests regarding rural Ireland would be satisfied by the Programme For Government.
"The programme was bad enough, but when we saw the announcement of the ministers, it was devastating. You take from Donegal right down to Kerry, and then to Clare and then on to Limerick, Tipperary, Waterford, Carlow, Kilkenny, and Wexford - no minister. It's unbelievable.
"With this kind of unequal spread of representation at government you’d wonder what planet Taoiseach Martin is on now."
Mr McGrath also described as "bizarre" some of the new government departments, such as the combination of social protection with rural development. "[The Taoiseach] must have just ruffled them up and pulled them out of a hat or something. It’s very, very shocking."
Niall Collins, Fianna Fáil TD for County Limerick, tweeted about his disappointment that there was "no representation at Cabinet level" for Limerick and Midwest.
Congratulations to @MichealMartinTD and my @fiannafailparty colleagues on being elected to new Government. Big challenges ahead. Limerick and Midwest very disappointed with no representation at Cabinet level. New Govt must address the needs of Limerick/Midwest to achieve balance.— Niall Collins (@NiallCollinsTD) June 29, 2020
Independent TD Michael Fitzmaurice, meanwhile, said the people of the west and northwest "have been left high and dry".
He said an even geographical spread of ministerial appointments is important to ensure an understanding of the country as a whole.
He said Mr Calleary's appointment as Government Chief Whip does not make up for the lack of Government ministers in the region.
"I have looked at the Constitution and the job of the Chief Whip is to organise the business of the day, organise the meeting of Cabinet and to organise votes, but they don't have a say, and they only speak when they're spoken to," the TD for Roscommon-Galway said.
Sinn Féin's Justice spokesperson Martin Kenny said anyone living in rural Ireland knows how the Government feels about them after the announcement of the new Cabinet, which does not include a single minister from Limerick to Donegal - but has six from Dublin.
The TD for Sligo-Leitrim said it was the "most glaring example of the neglect of rural Ireland" and described the "Dublin-centric Cabinet" as "sorely lacking in any regard for those of us west of the Shannon".
Earlier, Minister for Foreign Affairs and Defence Simon Coveney said he was very confident the voices of all communities across Ireland will be "heard and responded to" by the new Government.
Minister Coveney said there are people from the west of Ireland who are central to decision-making around the Cabinet table, including Mr Calleary and Ms Naughton.
He said it was not easy to get the balance right between geography, gender and matching people to very demanding portfolios and the party leaders "have done their best" to ensure that.
Mr Coveney said there will be some high-profile names from the west of Ireland among the junior ministerial appointments.
Additional reporting Conor Kane