The 49-year-old shrugged off suggestions the club would have trouble qualifying from Group D despite leaving it late to secure a point against their Bundesliga opposition
It took an 89th minute free-kick from Mesut Ozil to snatch a point for Los Merengues, after the German side had gone in ahead at the break through Marco Reus and an Alvaro Arbeloa own goal.
Mourinho believes his side finishing second in the group is a bigger concern for other clubs.
"If we qualify, if this is the most difficult group and we end up second, then, that's a problem for the other teams that end up first in their groups," Mourinho told reporters.
"The two times that I've won the Champions League my team ended the group stage in second place.
"There is no drama here. We played a great game versus Manchester City and today it's been another great game.
"We made two big defensive mistakes, you can't do that against a big team, they will kill you.
"Dortmund put us under a lot of pressure. In the first half we couldn't perform, but the second half was quite different, I liked the second half."
Los Blancos' trainer also brushed off a question about any hostility the crowd at the Bernabeu showed this evening.
He said: "After two years here I can't be surprised, whistles, support, a cold stadium ... it's a cultural issue."
When asked why Alvaro Morata was not in the squad after Karim Benzema was ruled out yesterday, he said: "Easy, I'm to blame for that. Morata played 90 minutes on Sunday. I didn't know I would not have Benzema and Pipa [Higuain].
"Benzema was injured during a training session, and then Pipa got injured in the first half.
"I was asked to let Morata play for Castilla and I said yes, so I'm to blame for not having him available today."
Mourinho then expressed his doubts that either Higuain or Benzema would be available for Madrid's Liga match against Levante on November 11.
"I guess that both Benzema and Pipa will not be available for Sunday."
Madrid's centre-back Pepe praised Dortmund after the match, but also took the opportunity to comment on the difficulty of Group D.
The 29-year-old, who scored his side's first goal, told reporters: "The first half was very open and I'm sure it was great for the spectators, but the second half was ours, against a great team.
"We are in a very difficult group, and we must keep on working."
The other two teams looking to qualify from Group D are Manchester City and Ajax, they also drew 2-2 tonight, despite the Dutch side leading 2-0 in the first half.
The Portugal international spoke of how Madrid must have faith in their ability with two rounds of matches left in the group stages.
"We still have to play against City [Manchester City]. We must trust ourselves, we're doing a great job."
The Liga champions face Roberto Mancini's side at the Etihad Stadium on November 21.