Donyell Malen had scored a superb goal for the visitors against his former side before Eindhoven's Luuk de Jong converted the spot kick in the 56th minute at the Philips Stadion.
"Zero per cent penalty, zero," Dortmund defender Mats Hummels said of his challenge on Malik Tillman.
"I go in for the tackle, I clearly get to the ball first, I change its course and then I make minimal contact. But this is football, I am sorry, zero penalty.
"Tillman was cracking up laughing, (Eindhoven winger Johan) Bakayoko also cracked up laughing, they all looked at me, grinning for several minutes," Hummels added.
The Dortmund defender got a touch on the ball before making contact with German-born US international Tillman but a VAR review confirmed the on-field decision by referee Srdjan Jovanovic, much to the visitors’ dismay.
"That is the second ridiculous penalty awarded against us in the Champions League after the (group game) at Paris St Germain. I don't understand the referees at the moment," Hummels said.
Dortmund lost 2-0 in Paris in September with Kylian Mbappe scoring from the spot following a handball incident.
Dortmund host the Dutch side on March 13th in the return leg.
"We asked him (referee) but for him, it was a clear-cut situation," Dortmund sports director Sebastian Kehl said of Eindhoven's penalty.
"You cannot change that but try to influence it through the fourth official. This is a very painful situation for us."
For coach Edin Terzic, the only thing to do was to move on.
"We cannot change it, it's part of the game," he added. "We now have the chance to make things right in three weeks. This is the only thing we control and we will focus on that."
Check out the full match report from the tie with Flashscore.
