Delaney's comments were made as Denmark were held to a goalless draw by the 'Green Army' on Saturday in the UEFA Nations League.
O'Neill repsonded to the midfielder, claiming: "It's not long ago that Denmark were considered a primitive side. Sometimes it's quite easy to make those sort of remarks.
"Denmark, who did exceptionally well in the World Cup, eventually didn't cause us many problems and they can play pretty primitively too - the centre forward [Cornelius], who's 6'7.
"If you asked teams around Europe, they'll say Eriksen, world class, Delaney's a top-quality player, little [Pione] Sisto plays in a big league as well in Spain.
"But they can dish it out themselves if necessary. They're as physical a side as you'll see in European football, so I wouldn't concern myself about other remarks."
O'Neill's side take on Wales in the Nations League on Tuesday, and will be facing relegation if they fail to pick up any points.