Andrew McGinely has said the decision to find Deirdre Morley not guilty of the murder of her three kids is "probably the right verdict".
In a statement issued on Thursday, Mr McGinley said he will "continue to celebrate the all too short lives of Conor, Darragh and Carla to ensure that they are never forgotten".
Earlier, Deirdre Morley was found not guilty by reason of insanity of the murder of her three young children.
The jury of ten men and two women reached their decision after four hours and 23 minutes of deliberations.
Mr McGinley said: "Today’s verdict is probably the right verdict. Everyone who knows Deirdre, knows how much she loved our children and how devoted she was to them.
"Whatever the outcome of this trial, it remains that our beloved children Conor, Darragh and Carla have died. As I write this, I’m no closer to understanding why."
The bereaved father sent a message to others in the hope that they will come forward and help avoid "similar catastrophic loss" - and said he will continue his work to make sure his kids aren't forgotten.
He added: "It is too late for us but I do not want to see another grieving parent speaking in the future about the same exclusion after a similar catastrophic loss. My message here and now to anyone who has a loved one in psychiatric care is to get in there as soon as you can to be added as an advocate for their treatment plan.
"I will continue to celebrate the all too short lives of Conor, Darragh and Carla to ensure that they are never forgotten. Conor had asked me to help him with a YouTube channel and I promised I would.
"You will find Conor’s Clips on YouTube now and given his interest in the internet this is supported on Twitter and Instagram. I hope to continue to do that with the same great sense of humour which Conor had.
"I promised to build a snowman for Carla. As we don’t get snow every year I’m planning a colouring competition called Snowman for Carla in her name.
"For Darragh I promised to get involved with Rathcoole Boys. However, Darragh had been involved in everything in the community – Rathcoole Boys, Commercials Hurling, St Marys GAA, The Athletics Club, the Drama Club to name but a few. In Darragh’s name I am starting a charity to encourage everyone to get involved more in their own communities and to participate ... As Darragh Did.
"Personally, I will be taking some of the unique characters that Conor and Darragh created in their own comics, plays and books and I will attempt to do them proud by bringing these characters further along in books which I hope to write in their honour.
He also thanked everyone involved in the trial, saying: "Thank you to everyone who has supported our families over the past year and more. We will never be able to thank you all enough. Thanks to the Office of the DPP, Anne Marie Lawlor, Grainne Whelan and Edel Gilligan.
"Also to Jonathan Dunphy and Michael Bowman for the Defence. Thanks to the Gardai and finally to the jury for the task they faced with this trial."
