Marco Reus put the German side in front from the spot early in the Group F clash after Robert Lewandowski was held in the box by Federico Fernandez.
Jakub Blaszczykowski notched a second on the hour-mark and Pierre-Emerick Aubameyang scored a third after Lorenzo Insigne had pulled one back for the Italians.
But Benitez feels the early goal was the turning point.
"Clearly the penalty changed everything," he told Sky Sport Italia. "I think we put in a great performance against one of Europe's top clubs.
"To start like that a goal down after 10 minutes, then we conceded a second just after we had the chance to equalise.
"The side showed character, intensity and played at a good level.
"The positive aspect is the great performance, intensity, grit and determination right to the end. I think the lads did great work.
"Did we allow Borussia too many scoring opportunities? That's because we were chasing the game.
"We need to think positive. This is a team that is still growing and for long periods tonight we had the kind of performance I want to see in Serie A.
"Let's not forget Borussia have played with the same coach (Jurgen Klopp) for six years and were in the Champions League final last season.
"I saw character today and the team wanted to score and win today, regardless of the venue. Obviously Borussia are very fast and talented, so they are tough to take on."
The result lifts Dortmund above Napoli owing to their better head-to-head record, and leaves the Serie A side needing to better their German opponents' result on the final matchday in a fortnight's time, or beat Arsenal by three clear goals.
