One of Leicester City, Arsenal, Monaco, Juventus or Napoli will stand in Real's way in the round of 16.
A double from Karim Benzema had Real well on course to leapfrog the Germans into top spot, but Pierre-Emerick Aubameyang halved Dortmund's deficit before teeing up Marco Reus for the equaliser two minutes from time.
However, that late goal could well benefit Real as they now can't face the likes of Bayern Munich, Manchester City or Paris Saint-Germain in Monday's draw.
Instead, one of Leicester City, Arsenal, Monaco, Juventus or Napoli will stand in Real's way come the new year.
"Juventus for two reasons," said Zidane, who joined Real from the Italian giants for a world record fee in 2001, when asked who he wants to avoid.
"I am very proud of the players and how they played against a great team with good players.
"We needed to be a bit more attentive in the final 10 minutes.
"We have to forget about it and move on. Given what we had done (in the group) until now it was logical that they finished top and us second."
A draw was enough, though, to extend Real's unbeaten run in all competitions since April to 34 games -- matching a club record.
However, the Frenchman refused to take credit despite inspiring a huge turnaround in fortunes for the Spanish giants since taking his first senior managerial role in January.
"You have to congratulate the players. They are the ones that are on the pitch, that have to fight and run," he added.
"The fans too because they are always behind the team, they are always cheering.
"And everyone around the club. The idea is to continue what we are doing but there is still a long way to go."
Reus's late strike was a huge boost to Dortmund's chances of progression as they can now face PSG, Benfica, Man City, Sevilla or Porto in the last 16.
And Dortmund boss Thomas Tuchel insisted the dramatic nature of the game showed there had been no pact to settle for a mutually beneficial draw.
"We didn't do some tactical calculation," said Tuchel.
"We can have no influence in the draw, but against any opponents we will play to our limit to reach the next stage."
Dortmund looked set to pay for their profligacy in front of goal as they missed a host of clear chances in between Benzema's two goals with American wonder kid Christian Pulisic and Gonzalo Castro especially culpable.
However, Aubameyang was far more deadly as he slotted home his 18th goal in as many games this season before teeing up substitute Reus, who only missed out on starting due to a cold.
"I wasn't feeling great the last few days, I wanted to start, but the risk was too high," said Reus.
"Real had some big chances in the second half, but we hoped for a lucky punch and we got it.
"Auba was world-class with his pass and I was happy to get on the end of it -- the goal was 99 percent him and one from me."