Lee Carsley insisted that the decision to go through with his pledge not to sing the English national anthem ahead of his first game as interim head coach does not make him “any less committed” to do the job.

Goals from Declan Rice and Jack Grealish in the first half set up a comfortable victory for England over the Republic of Ireland in the Nations League. Carsley, who was born in Birmingham and won 40 Ireland caps having qualified through a grandmother, had been criticised in some quarters after admitting that he would not change his pre-match routine by singing God Save the King because he wants to “focus on the football”.

The 50-year-old’s name was booed by a section of the home supporters when it was read out before kick-off, as well as those of Rice and Grealish. Both switched allegiances to England despite representing Ireland with age-group teams and also – in Rice’s case – at senior level.

Related: Rice and Grealish start new England era with Nations League victory in Ireland

But having emerged from the tunnel just before kickoff, Carsley instead headed for the home team’s bench and sat down before being tapped on the shoulder by a steward and was informed of his mistake.

The former manager of England’s Under 21 side – who has replaced Gareth Southgate at least for the Nations League campaign – did not look amused as he made his way to the away dugout. But Carsley remained true to his word about not singing the anthem, which was booed loudly by the home supporters on England’s first visit to the Irish capital since 2015.

“No, it’s definitely not affected my day or my preparations,” said Carsley of the furore surrounding his decision not to sing the national anthem. “I found out about it this morning. I fully respect people’s opinions – it’s something that I’ve never done. I fully respect both national anthems.

“Today was one of the proudest days of my life to lead an England team out in Dublin. I don’t feel hard done by or aggrieved. I’ve played in teams where players are belting out the anthem next to me but I’ve also played in teams where players or coaches don’t sing. I don’t think it makes me any less committed. I was looking forward so much to today and it’s the proudest day of my football career. You couldn’t have written it really.”

Asked whether the reaction had put him off going for the permanent role, he added: “I would never judge anyone for singing or not. I had a great experience when I played for the Republic of Ireland and I’m having a great experience now – the responsibility that I’ve got of being head coach of the senior team. You have to accept that with that comes a bit of judgement – I don’t feel hard done by.”

On his faux pas of sitting in the wrong dugout, Carley could see the funny side. “I did go down the tunnel and turn right – as you know I’ve spent a lot of time on the bench so I know exactly where that is,” he said. “I realised that the coaches were all on the other bench so it was quickly resolved.”

There had been loud boos reserved for Rice and Grealish when the two teams were first read out an hour before the start. Those intensified as the teams prepared to kick off, with a banner that appeared to be directed at the Arsenal and Manchester City players proclaiming that “The snakes are back.”

Rice made a point of not celebrating when he opened the scoring in the 11th minute but was still greeted by more boos. There was no holding back from Grealish – who was left out of Southgate’s Euro 2024 squad – when he doubled the lead and he held both arms aloft to acclaim the travelling supporters as England went on to record their first win in Dublin for 60 years.

“It was what me and Declan expected,” admitted Grealish afterwards. “We have nothing bad to say, we both enjoyed our time [playing for Ireland] – I certainly did and I have a lot of Irish in my family, so there’s no bad blood whatsoever from my side.”