The Football Association of Ireland (FAI) and national team manager Vera Pauw apologised on Wednesday for players singing a song referencing the IRA after they beat Scotland 1-0 and qualified for the women's World Cup finals for the first time.
A video posted on social media after the match on Tuesday showed the squad singing "Ooh ah, up the 'RA", a song supportive of the paramilitary Irish Republican Army that sought to end British rule in Northern Ireland.
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UEFA have opened an investigation into "potential inappropriate behaviour" by Ireland players.
"The first thing in our team is respect for the people around us," Ireland's Dutch manager Pauw told Sky Sports.
"We have done something that hurt people and it's no excuse that we did not mean to hurt anyone. It's not an excuse that we were celebrating."
Pauw said the players were devastated and the one who posted the video was "crying in her room because she hurt people and she never meant it."
Pauw said she was not in the dressing room and, as a foreign coach, would not have been aware what was sung even if she had been but took full responsibility regardless.
"It's wrong, we shouldn't have done it and we will never do it again," she said.
The FAI apologised in a statement for any offence caused after the match at Glasgow's Hampden Park stadium.
Defender Chloe Mustaki said the entire squad felt embarrassed.
"There was quite a lot going on in the changing room in such a major moment and there were lots of different songs being put on left, right and centre so we're incredibly embarrassed," she said.
"We didn't mean any hurt on our end so we do really apologise for that."