Villarreal made seven changes from their previous outing and set up ambitiously for their return to the Champions League, but were undone by a Renato Veiga own goal, a disputed penalty converted by Serhou Guirassy and a second Guirassy own goal in stoppage time that ultimately proved decisive despite Santiago Mouriño's equaliser and a battling finish at Signal Iduna Park.
"I think it was a very good performance from the team, but you leave disappointed with the result," Pérez said.
"Despite the good feelings, we have to improve our composure with everything we create, and defend better, because today they scored three goals against us again."
The head coach felt the scale of the challenge made the display all the more creditable.
"The difficulty was very high given where we're coming from, the team we were facing and the atmosphere. I could say I'm proud of how we approached it, but we have to improve."
Pérez pointed to fine margins rather than a lack of effort or belief as the difference between the sides.
"It's frustrating because the team is executing the idea with conviction and not getting what it deserves. But I'm convinced this is the right path and that we must persist with it, because it's the right one," he said.
Villarreal remain without a win under their new head coach since returning to the competition, but Pérez's insistence on staying the course suggests no immediate change in approach despite back-to-back matches conceding three goals.
Asked about the contentious penalty awarded to Borussia Dortmund following a coming-together between Guirassy and Mouriño in the box, Pérez declined to comment, sticking to his usual policy of not discussing refereeing decisions.
The result means Villarreal's return to the Champions League after a period away from the competition has begun without a point, a frustrating outcome given the chances created against a Dortmund side that has scored freely across its opening matches.
Pérez's approach this season has centred on an aggressive, front-foot style regardless of opponent, and Tuesday's performance offered evidence that the underlying process is sound even if results have not yet followed, with the same defensive fragility that undid Villarreal against Dortmund having also cost them points domestically in recent weeks.
The head coach will hope his side's next continental outing brings the improved sharpness and defensive discipline he identified as missing at Signal Iduna Park.