Aberdeen travelled to the Netherlands after a goalless draw at Pittodrie last week, with some Dutch players suggesting ahead of the second leg they had one foot in the next round.
But an Adam Rooney penalty and Niall McGinn strike gave the Dons a dream start, with Maikel Kieftenbeld's goal the only response from the hosts.
Aberdeen now face La Liga cracks Real Sociedad next week in Spain as their European adventure continues.
"We went about our business well," said McInnes.
"We would never treat any of our opponents lightly. If anyone treats us lightly they could come undone.
"We showed a lot of different aspects to our game. We showed pace, invention on the break, good confidence in the final third at times.
"Then, when it was required, real resolve and determination and organisation to see the game out.
"Other than a 20 minute period when they had a bit of momentum I thought it was a very comfortable night's work. I'm not surprised, I felt we could get the result.
"I feel we've got a good team, there's lots to look forward to this season and beyond."
Source: BBC Sport