Naomi Long, who is a Christian, has been speaking after the deputy first minister announced his resignation - signalling the end of the power-sharing government.
Sinn Fein's Martin McGuinness is demanding fresh elections in protest at the DUP's handling of an energy initiative, which has seen costs spiral.
He'd previously called for DUP's Arlene Foster, the first minister to resign.
Seven days of talks at pulling the government back together will now take place and if no resolution can be found, the country will face another election.
"I don't think the public in Northern Ireland will be impressed that those who they elected to do this job have failed so abysmally to sort out the normal business of government which they ought to be able to do as a matter of routine," Naomi Long told Premier.
"I suspect the confidence they have in the institutions, which was already at an all-time low, has probably dropped further with this announcement today."
Mr McGuinness said he was resigning with "deep regret and reluctance".
"The First Minister has refused to stand aside, without prejudice, pending a preliminary report from an investigation," he said. "That position is not credible or tenable."
Sinn Fein will not replace him in the role, which means another election is likely.
Mrs Foster had previously rejected calls for her to reisign. Earlier in the day she said: "If he is playing a game of chicken, if Sinn Fein are playing a game of chicken, and they think we are going to blink in relation to me stepping aside they are wrong - I won't be stepping aside.
"And if there is an election, there is an election."
Listen to Naomi Long speaking to Premier's Marcus Jones