The game had hardly got going when Denmark took the lead on nine minutes through Nicoline Sorensen, when the ball fell kindly to her unmarked inside the penalty area and she fired in.
Ireland attempted to respond by pressing their opponents high with Amber Barrett and Heather Payne both working incredibly hard to force the Danish backline into mistakes.
The more pressure that Ireland applied, the more vulnerable Denmark looked as they misplaced passes and left gaps between the lines. But the final pass or breakaway evaded the home team.
On 53 minutes, Katie McCabe cut inside and unloaded a shot from distance. As it glided through the air, Danish goalkeeper Lene Christensen could only look on as it smashed back off the crossbar.
A number of changes gave Ireland some extra energy with Emily Whelan and Ellen Molloy introducing a spark to the attacking play. The latter fired wide with a shot from distance.
At the other end, goalkeeper Grace Moloney had to be at her best on 68 minutes to deny Signe Bruun following a swift counter attack from Denmark. It was a fine save from the Reading stopper.
Moloney was at it again on 76 minutes to deny Sorensen, but Ireland finished strongly as they went in search of a goal to level matters. It didn't come but the effort was laudable.
This is clearly an Ireland team that is moving in the right direction, under Pauw's watch, and next up is a friendly away to Belgium.
Republic of Ireland: Moloney; Keenan (O’Gorman 72), Fahey, Quinn, Caldwell, McCabe; Finn, Connolly (Molloy 61), O’Sullivan; Payne (Whelan 46), Barrett (Jarrett 61).
Denmark: Christensen; Sevecke, Boye, Veje (Gevitz 72); Sorensen, Junge, Troelsgaard, Svava (Troelsgaard 61); Harder (Larsen 80), Bruun (Muller Holdt 72), Nadim.
Referee: Louise Thompson (NIR).