Ireland manager O’Neill, who became the first man to guide the nation into the knockout rounds at the European Championship, was quick to plant his feet firmly on the ground when asked about his team’s prospects in the last 16.

He said with a smile: “It is definite we are playing France, isn’t it? Mmmm…easy.”

O’Neill could hardly have been more delighted with what he saw from his players as they took the game to a much-changed Italy team from the off and were denied what looked like a clear penalty just before half-time when James McClean went down under a challenge from Federico Bernardeschi.

However, they kept going and got their reward when, seconds after substitute Wes Hoolahan had missed a glorious opportunity to win it himself, he crossed for Brady to head home.

O’Neill said: “It was a great win. We deserved to win the game – I thought the chance had gone when the goalkeeper saved from Wes and I didn’t want it to be one of those nights.

“It looked as if we should have had a penalty – it was pretty clear-cut – but it doesn’t matter now. We have won the game, we deserved to win it and we dominated for incredible periods of the game and played some phenomenal stuff.”

Italy boss Antonio Conte, who rested eight players having seen his team already secure top spot in Group E with wins over Belgium and Sweden, congratulated Ireland on their progression even if he did have a slightly different view of what he had just witnessed.

Conte, whose side will play Spain at the Stade de France on Monday, said: “I think the pitch definitely helped them more in this sort of situation than it did us, but I have to congratulate them because they have really put a lot into the game, a lot of grit because this was life and death for them.

“Perhaps we were punished when we were on top of the game, that’s when we conceded. Congratulations to the Republic of Ireland because they really wanted to go through and they were rewarded, perhaps more than they deserved to, but they were rewarded nonetheless.”

Conte will begin preparations for the Spain game on Thursday, but would not be drawn into analysing the reigning champions.

He said: “We are definitely playing against one of the top sides in the world, so what do I need to say about Spain?

“Do you want me to say they are rubbish? Tell me, do you want me to tell you they are rubbish? We are talking about one of the best sides in the world, end of.”