Perhaps, Lee Carsley was simply consumed by his focus on the opening minutes of his first game in interim charge of England. Because when the manager emerged to take his seat before kick-off and, yes, before the anthems, he turned right instead of left and sat down on the Republic of Ireland bench.

Old habits die hard for the former Ireland midfielder and he looked nonplussed when the error was pointed out and he was ushered towards his correct place. Yet if that felt like a bad omen, nobody connected to England ought to have worried.

As advertised, Carsley remained stony-faced when God Save the King played but what would have thrilled him as he began what is effectively a six-game audition for the permanent job was the first-half performance of his team.

It was always going to be a hot occasion for Declan Rice and Jack Grealish, the one-time Ireland internationals who subsequently switched their allegiances.

Related: Republic of Ireland 0-2 England: Nations League player ratings

Carsley was also booed by the home crowd. But it was Rice and Grealish who got the goals that put England in control before the interval, who were the most eye-catching performers during that impressive period, and it allowed England to coast to victory during a more pedestrian second half.

England had been infamously stodgy under Gareth Southgate at Euro 2024, albeit as they reached the final and, if anything, Carsley needed a performance here more than a result. He certainly got that in the first half. A new era has its foundation stone.

The first loud boos for Rice and Grealish had come when the teams were read out around 40 minutes before kick-off and that was when there were only a smattering of fans inside the ground. “The snakes are back,” went the wording on one banner in the home seats. And then, of course, we had Carsley and anthem-gate.

Carsley, who was never going to sing, felt the burn of the TV cameras and there had to have been times during this very particular England storm when he has reflected on how the football is only a part of his new office. How does he feel about that?

The game was much bigger than it would have been before England’s managerial handover from Southgate, Carsley the focus of plenty of the attention.

“Lee, you’re one result away from being an Irish legend,” read a billboard in town from a gimmicky bookmaker.

The decibel levels rose sharply whenever Rice or Grealish had possession but neither of them shrank. From far it.

Grealish, playing to the left of a central midfield three, demanded the ball from the first whistle, looking to carry it, invite the challenges, the confrontations, too, and it just had to be Rice with the breakthrough goal.

Trent Alexander-Arnold was prominent, stepping up from right-back into midfield, his passing on point. He had already teed up Harry Kane for a free header – the captain headed high – when he sent Anthony Gordon clean through. Caoimhín Kelleher saved but Gordon recycled the move, crossing low for Kane, who was stopped by Nathan Collins’s block tackle. When the ball broke, Rice lashed high into the net.

Ireland had flickered in the opening minutes. Jayson Molumby headed over from a corner; Sammie Szmodics worked Jordan Pickford. They tried to push but the difference in technical quality was quickly apparent. Carsley could be pleased with how England manipulated the ball. They found spaces in front of the Ireland defence and up the channels, Gordon a threat off the left. The movement and rotations were fluid.

Carsley gave Rice a right-sided No 8 role, Kobbie Mainoo holding in front of the back four, and Rice enjoyed himself when he could lengthen his stride.

There were 15 minutes on the clock when he led a box-to-box counter, feeding Gordon, who crossed for Kane. It looked like being a routine close finish for Kane only for Kelleher to make an excellent block.

Rice’s celebrations upon his goal were controlled, muted. Not so those of Grealish, who lapped up the applause of the England fans behind the goal. Rice was central to the buildup, playing give-and-goes with first Mainoo and then Bukayo Saka before crossing low for Grealish, who angled a right-footed finish inside the far corner.

Gordon might have scored after the half-hour on another incisive England move and there were boos from the Ireland support at half-time for a different reason; they were frustrated with their team.

The atmosphere was notably subdued upon the second-half restart. It had been difficult to locate any pre-match optimism among the Ireland fanbase and it was as if the realisation had set in that they could be in for a long second period. Irish football is at an extremely low ebb; everybody feels beaten down by the years of disappointment.

Related: England’s Lee Carsley keeps national anthem pledge and sits on wrong bench

The new manager, Heimir Hallgrímsson, needed a spark. He adjusted Szmodics’s position just before the hour, moving him inside from the wing, getting him closer to the striker, Adam Idah. Szmodics had a few moments, especially the one when he slammed a shot off target after a pull-back from Chiedozie Ogbene. He also set up Molumby, who shot wildly.

• Download the Guardian app from the iOS App Store on iPhone or the Google Play store on Android by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the Menu button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

England’s intensity dropped and it felt as though Carsley needed to make substitutions. Strangely, he waited until the 76th minute when, as part of a triple change, he ­introduced Angel Gomes and Morgan Gibbs-White for their debuts. One of the players he withdrew was Grealish, who applauded the England fans and departed at low speed. He had enjoyed himself.

England might have scored again. The substitute Jarrod Bowen was twice denied by Kelleher, the second at point-blank range, while the goalkeeper also saved smartly from Saka. England and Carsley had enough.