Michael Krohn-Dehli’s first half goal proved enough to overcome Bert van Marwijk's team and boost the confidence of Morten Olsen’s men ahead of the final two matches of a tough Group B campaign.
Aware of the impressive nature of Denmark’s triumph, Bendtner maintains the most important thing is that his country managed to pick up the three points.
"Starting the group really well is what we dreamed of, and taking the lead in the first half was really good for us," Bentdner told Arsenal's official website.
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"But the luck was on our side and we took full advantage of that."
Bendtner also praised his side’s impressive defensive performance, with Denmark successfully managing to block out a number of offensive waves directed at Stephan Andersen's goal.
"I was quite pleased," Bendtner added. "As a striker you’d always like to have one or two chances to score and on another day I probably would have, but I’m proud and happy that I can defend from the front and help the team that way as well."
The game’s only goal came against the run of play, with the Krohn-Dehli's angled strike beating Maarten Stekelenburg and hitting the back of the Dutch net half way through the first period.
"We had our game plan, and I think when they tried to play it out from the back we stood up really well," Bendtner continued.
"We made it difficult for them to play through us. It was only when we gave the ball away in the middle of the park that they were able to counter-attack, because we were out of position.
"Our centre-backs [Daniel Agger and Simon Kjaer] were strong. They were up against a difficult test today and I think they did well to keep the score at 1-0."
Denmark must now look onwards to their next match, which takes place on Wednesday against Portugal. Paulo Bento's team endured a narrow 1-0 defeat at the hands of a muted Germany side on Saturday evening.
"If we beat Portugal it’d be a massive result, but we cannot think about anything more right now," Bendtner said.
"We have to keep believing that we can get something out of the next game because three points will not be enough to qualify.
"We have started well and it’s nice to have got the first game out of the way – that’s always a little bit nervy because we’ve prepared such a long time for it. Now we just look forward to Porgual match."