Napoli needed to get their Group F campaign off to a winning start considering Manchester City are also in their pool but they came unstuck with Shakhtar good value for the three points.
Taison and Facundo Ferreyra put Shakhtar in front before Arkadiusz Milik's penalty made a fight of the closing stages, where Napoli had chances to grab an equaliser.
However they could not find it, much to the frustration of Insigne.
"We knew that Shakhtar were a good side as they have quality players in attack," he told Mediaset Premium. "I honestly don't know what we got wrong and why we played like this.
"During the week, we will discuss it with the coach and see what mistakes we made so that we can correct them. Perhaps we believed a little too late that we could come back, but we had chances and didn't make the most of them. We had the opportunities to equalise. It's a pity.
"We've got to get our heads down and work hard to improve on the errors we saw today."