Capped three times in senior international friendly games by Martin O’Neill, London-born Rice has made his intentions clear to switch allegiances to England.
McCarthy said: "Declan Rice rang me today and told me he has decided to give it a go with England. Good luck to him, it is his decision and his decision alone and I wish him well with his international career in the future.
"When I met Declan and his family, along with Robbie Keane last November, I told Declan that I would be delighted if he opted to stay with Ireland having won three senior caps and represented us so many times at underage level.
“That is not to be. I never got the chance to work with Declan so he is not my player and won’t be now that he has made up his mind.
"We start the European Championship qualifiers at the end of March and my coaching staff and I have concentrated our efforts on those who want to play for us. They are the important ones and they are the ones who want to play for Ireland against Gibraltar and Georgia.
"We know Declan’s decision now and we continue to plan for the games next month."
Ireland boss McCarthy has also praised FAI scout Mark O’Toole, who discovered Rice as a teenager and introduced him to the Ireland Under-16 squad back in 2015.
McCarthy added: "I phoned Mark [O'Toole] and he is disappointed with this news. I feel for Mark because he found him for us and nurtured Declan as a player and helped develop his career, something Declan has publicly thanked him for in the recent past.
"But this is Declan’s decision. We have availed of the ruling ourselves so we can’t complain about it. We will concentrate on the games in March."
Rice represented Ireland from Under-16s up to senior level and won International Player of the Year at U-17 & U-19 level.