The Boys in Green, ranked seven places below their opponents in the latest FIFA rankings, had just 28% possession in Copenhagen but held on for a stalemate.
"I thought it was a tough evening for us and the players did splendidly," Sky Sports News quotes him as saying. "They put a lot of effort in and it's all to play for now. We have to win a game. And I think we have to score a couple of goals because Denmark are capable of scoring too. I'm not so sure they had so many chances.
"Darren [Randolph] has been playing particularly well for us, but overall we restricted them, though we need to be more creative ourselves. We didn't score a goal obviously, but we're still in the tie.
"Control is when you have the ball, but they had the ball and were trying to probe for openings. But when we closed them down they lost their way a little bit. There's everything to go for on Tuesday night."
Ireland are now unbeaten in their last four playoff qualifiers away from home, winning one and drawing three.