The controversial 'Golfgate' dinner resulted in a number of resignations including that of former Minister for Agriculture Dara Calleary and former EU commissioner Phil Hogan.
Speaking for the first time since the event two weeks ago, the Fine Gael Senator apologised for his lapse of judgement, saying he understands the hurt and anger he has caused people.
Senator Cummins lost the Fine Gael party whip after it emerged he was one of 80 people in attendance at the event in Clifden which allegedly breached Covid-19 restrictions.
Following the event, Gardaí launched an investigation to determine if public health measures were flouted at the dinner held in the Station House Hotel.
Senator Cummins told WLR that he does not feel that resigning is the right thing to do.
"I've never been in a situation like this. It's knocked me and my family for six. I've struggled with it, but I'm not looking for sympathy because I understand the hurt and anger that I have caused people," he said.
Meanwhile, the coalition leaders are yet to nominate a replacement for Phil Hogan to the EU Commission.
Following the resignation of Mr Hogan, President of the Commission, Ursula von der Leyen invited the Government to nominate a male and a female candidate for the position.
Taoiseach Micheál Martin has said there is no strain between him and Ms von der Leyen despite delays in the nominations being made.
Mr Martin confirmed that two candidates will be put forward within the next two days.