But then, manic Monday at the Aviva was one of those nights when, in terms of the consequences of the result, a draw most definitely felt like a defeat.

“Yeah, in terms of not qualifying,” McCarthy agreed.

“It hurts when you’ve played well. I think we could have won the game and, overall, we should have won the game. That does hurt but, no, I wouldn’t want to get thrashed by four or five. That would hurt a lot more, if I was stood here trying to justify a 4-0 defeat. I think that would be tough.”

Still, it was tough enough on Monday night for the mood in the dressing room afterwards to be one wholly dominated by thoughts of what so nearly might have been.

“Well, they were all very disappointed because, while we’re not out of the competition, they saw the chance that we had to win it. That’s going to be galling for all of us. But I said to them I was immensely proud of them. I told them. I think they’re brilliant, they gave me absolutely everything. I’ve no criticism of them at all. I thought the goal was a bit soft we gave away, but the response was brilliant.”

McCarthy firmly rebuffed the notion that he had set out to contain the Danes before allowing his team to have a go at them.

“I wasn’t trying to play cagey at all, that wasn’t the case,” he said.

We were playing against a very good team and I didn’t want to be 1-0 down. You know, ‘let’s all go gung-ho’ and they catch us on the break and do us and we go 1-0 down in the first 15 minutes and the crowd is dead and everything is dead. We probably don’t have that response then.

"So it was important that we stayed in the game against them.

“There was never going to be that many chances, I don’t think, and we had the best one with Conor (Hourihane) when he got in. He didn’t catch it as well as he would have liked to. And then there was one from the corner kick when Duffer (Shane Duffy) got in. But they didn’t have many chances either.

“I was pleased with the way lads adhered to the gameplan and played it out. The Danes didn’t have as much possession in the first half as they did in Denmark and I was pleased with that. All this about going with an extra striker, you know, I don’t get it, really.”

While Ireland are no strangers to play-offs, McCarthy and his players this time find themselves in the unaccustomed position of having to get through the whole of a winter before they can go for their second and, hopefully, third bite of the cherry. But the manager thinks the protracted build-up could have its benefits.

“Possibly. I think the disappointment of drawing the game and not qualifying for the Euros will be a lot less in March. They have Christmas, and all the games they play over Christmas and then it’s into January. They will be forgetting all of what has happened here on Monday and when they come back in March they will be fresh for two games, so that might be a positive as well.

“The negatives? I don’t look for them. I seriously don’t look for them. Everyone else puts negatives in my way. If that’s what we have to do, then get out and do it as the best you can and don’t whinge that it’s in March. Don’t look for that at all. We’ll put a team together and whoever is fit and ready to go in March, I’ll pick the best team I possibly can.”

Assuming he is available, one of the nailed-on starters will be David McGoldrick, whose influential performance on Monday night underlined just how badly he had been missed in the preceding qualifiers in Tbilisi and Geneva.

“He is our best striker, there is no doubt about it,” declared McCarthy. “I’m saying that and that’s not being detrimental to all of the other lads, because I think they would recognise that as well. They’d all recognise that I think it, because I keep playing him, so it’s as plain as the nose on my face. When March comes around, let’s hope he’s fit.

“Let’s hope Troy (Parrott) gets into the team, let’s hope he plays somewhere and gets some football, we’d have another one. Seanie Maguire came on against Denmark and was excellent too, so we have some options.”

And at the other end of the pitch, a big call McCarthy might have to make come spring is between Matt Doherty and Seamus Coleman, especially if the latter hasn’t reclaimed his place in the Everton team by then.

“It’s all hypothetical, isn’t it?” was the understandable response from the manager.

The Doc was great on Monday night. He played really well. We knew he was a good player and there is never anybody doubting his ability. It’s been a tight call all the time, it’s just my preference was Seamus. But we don’t know what March is going to bring. When I get the players together, I’ll know who is fit and ready to go. Wait and see.

“I’m not going to make a story of what full-back I’m going to play in March when we’re in November.”

Denmark boss Age Hariede, while relieved to be dodging what he called “the chaos” of the play-offs — “I’m glad to miss it, yes, absolutely!” — said he has seen enough improvement under McCarthy’s leadership to suggest that Ireland will be joining his team in the Euro 2020 finals.

“Definitely, there is more spirit in the side with almost the same players,” he said. “The lack of spirit (last year), you could see it and there was no enthusiasm, which is always there in Irish sides.

“I played against Irish sides myself and I know that there was always a lot of enthusiasm, they get the crowd behind the team.

“Now, they are really enthusiastic and I think some of the players have also improved. A lot of the players in this side come from the Premier League and they do well, and the clubs they play for also do well.

“Ireland have been steady through the campaign and they did well against Switzerland and played well against us the other night. So I think that they have a good chance of going through.”

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