Manchester City’s Vivianne Miedema opened the scoring for the Dutch in first-half stoppage time before Victoria Pelova doubled their tally after the break in the 48th minute to put the tie beyond doubt.
Barcelona forward Esmee Brugts added the extras as Wales opened with a heavy loss.
“It was a tough game. We know we’re in a hard group but, equally, it’s about Wales showing up and showing who we are as a team and a country,” Wilkinson told the BBC.
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“Getting into the half at 0-0 would have gone a long way. In the second half, that quick goal definitely hurt us.”
Wales will need to get points on the board against France in St Gallen on Wednesday if they are to progress from Group D.
They then face the Lionesses in their final group game as they bid for silverware in Switzerland.
“We’re going to have to grow and learn from this,” she added. “We’re looking forward to the next game now.”
Wales failed to register a shot on target in the match, and midfielder Jess Fishlock pointed towards Miedema’s 100th international goal and Pelova’s effort early in the second half as the turning points.
“To concede just before half-time and then so quickly after half-time, probably lapses of concentration and at this level, you switch off and you get punished,” Fishlock told the BBC.
“We are probably going to be a little bit disappointed in ourselves that we didn’t get in and regroup the way we normally do. But this is the level and we have to get used to it real fast.
“What I do know is that we are going to regroup and get better as this tournament goes on. I think we have learned we can’t switch off and we have to be better on the ball.
“At this level you have to keep the ball and move the ball and create space. We’ll figure it out.”
