Minister for Foreign Affairs Simon Coveney believes apologies issued over the Irish team's post match celebration in Glasgow are sincere.
Footage posted on social media after Ireland's historic 1-0 victory over Scotland showed players singing a pro-IRA chant in the dressing room at Hampden Park.
The FAI issued an apology following the controversy surrounding the singing. Manager Vera Pauw and players also addressed the matter, apologising for any offence caused.
Speaking in Belfast, Mr Coveney said the players made a mistake and it shouldn't have happened.
"I haven't seen the footage, but I have, of course, heard about it," Mr Conveney said.
"What I have seen is the apology from Vera Pauw, and from the FAI and also from a number of players.
"I think that those apologies are very sincere, Vera Pauw has said that she apologises from the bottom of her heart for offence caused.
"This is a group of people who are very tight and close-knit. Clearly there was a mistake made after the match last night, that shouldn't have happened.
"I think it's acknowledged, and there's a very sincere apology made, and I hope we can move on from that now, because last night was about spotty primarily, an extraordinary achievement by a group of people," Mr Coveney added.
Other politicians have also spoken on the controversial chanting.
Doug Beattie, leader of the Ulster Unionist Party, said the players had "let themselves down".
"An apology is the least that they can do," Mr Beattie said.
Michelle O'Neill, deputy leader of Sinn Féin, praised the achievement of Irish team, and hoped that a line could drawn under the matter.
"The FAI and the girls themselves have dealt with it in the media," she said.
Tuesday night's results means that Ireland's women's team will play at a major tournament for the first time ever next year.
