The first match of the two-leg tie for a place in the finals in Russia was a frustrating one for Denmark, who were held to a 0-0 draw at home.
And they will now try to seal a spot in the tournament with victory in the return leg in Dublin.
But Leicester City goalkeeper Schmeichel criticised the state of the pitch at Parken Stadium, telling Sky Sports: "It was a horrendous pitch, it was very disappointing from our point of view
"I've heard the Irish pitch is a bit better, so hopefully we can get our game going a little more over there.
"There was no grass on it. No grass and it was soft. It reminded of the old days in Bury in League Two and that kind of pitch. It was the same for both teams, but it is disappointing for such a big game.
"We tried to play fast football, but we had to take an extra touch all the time to hold on to the ball. It made a little difference, but that's no excuse. It was the same for both teams."
Opposite number Darren Randolph put in a superb performance for Ireland, making a string of saves that saw Schmeichel applaud the Middlesbrough keeper after the match.
"Randolph made some great saves so we're a little disappointed not to have won, but it's not the end of the world," he said.
"They were very disciplined and had the clear aim of stopping us scoring. When you see the opposition keeper being the man of the match, it tells you the story.
"It was a great performance from him. He's made a great double save and that could have opened it up. All credit to him. I hope he doesn't do that again!"
Ireland host Denmark for the return leg at the Aviva Stadium in Dublin on Tuesday, November 14.