The Labour leader, who was in New York, dismissed suggestions he had failed to support Ms Shortall in her dispute with Health Minister James Reilly.
“She had my support at every stage, she had the support of the Government,” he told RTÉ news, insisting he was “not going to get into a blame game”.
On Wednesday evening Ms Shortall became the fourth Labour TD to resign or lose the party whip. But Mr Gilmore said coalition is never easy.
“Yes it is difficult. Yes I understand very fully the political difficulties that are associated with it. But we are not going to be deflected from the job that we undertook,” he said.
Longford-Westmeath TD, Will Penrose, who resigned as Minister for Housing last year, said Ms Shortall’s decision was “a warning shot across the bows of Government” that Labour was “not there to be walked upon or rolled over”.
He told Midlands 103 Radio: “We are sent there with a particular ethos, negotiated in good faith in the programme that we want to see implemented. If there’s arrogance on behalf of anyone in Government that will ultimately lead to extreme difficulties.”
Taoiseach Enda Kenny refused to rule out further resignations over unpopular decisions that lay ahead, saying that “one can never speak of the future.”
Speaking at the ploughing championships in Wexford, he said: “Both parties in government have signed on for our Programme for Government. We recognise the difficulties and the challenges that lie ahead and I expect all ministers to play their part in implementing the Programme for Government.”
The Taoiseach said the health service was “not lacking direction” and was “part of the focus of government”.
“Minister Reilly has got the most difficult job in government as a frontline minister in terms of the changes that he has to make and that he is required to make.”
Mr White — a Dublin South TD and chairman of the Oireachtas finance committee — is expected to be formally appointed at next Tuesday’s Cabinet meeting.
Minister for Public Expenditure Brendan Howlin said it was a “blow” to lose Ms Shortall and that he “would have loved her to continue in the important role”.