O'Neill remains unbowed in the face of increasing pressure after Tuesday night's home defeat by Wales left Ireland on the brink of relegation from Nations League B.
Asked if he was facing the biggest challenge of his time in charge, which is due to pass five years next month, he replied: "Of course. Absolutely. It's definitely a challenge and it's a challenge I'm up for.
"Regardless of what people think, I've never shirked the responsibility. I've never really turned on my players - not that I need to, not with the effort they put into the games, which is phenomenal. We're short of some things, but in terms of spirit, drive and determination, it's absolutely there. We can turn the corner."
Ireland have now taken just a single point from their three Nations League games and head for Denmark next month knowing they could already have dropped into League C by the time they kick off in Aarhus.
That would mean a lower seeding for the Euro 2020 qualifiers, but O'Neill insists the task would not be significantly more difficult.
He said: "We were fourth seeds in the World Cup and we got through to the play-offs, so it hasn't been a real problem. You look at some of the sides who might be seeded third and you could turn around and think there's not a phenomenal difference. All I know is in my time here, in the World Cup draw and the Euros, the draws are difficult for us anyway. But I don't think it will make a significant difference."
Despite that, the 66-year-old remains convinced that the Republic not only can, but will, qualify for the finals.
Asked what gave him such confidence, he replied: "Because I'm good. I don't think I could have made a career out of management if I didn't have hunger and determination, the same approach I had as a professional player."
