A win for Real, who lost 2-1 away to the Bundesliga side last month, would have put them top of the group with two games to play.
However, they were twice undone by swift Dortmund counter-attacks and were fortunate to emerge with a point thanks to Ozil's 89th-minute effort that squeaked in off a post.
Mourinho, who is seeking to win Europe's elite club competition with a third club after triumphs with Porto in 2004 and Inter Milan two years ago, said history had shown topping the group was not necessarily a pre-requisite for success.
"The two times I won the Champions League I finished second in the group," he told a news conference.
"With Porto we were second and Real Madrid were first and we went on to play Manchester United and we got through," added the Portuguese, who also had a successful spell at Chelsea.
"With Inter we got Chelsea in the last 16. Chelsea out and we progressed. I am not superstitious but this makes me think that it doesn't matter whether you are first or second."
With four of six matches played the group thought to be the toughest in the competition is wide open.
Dortmund have eight points, with Real on seven, Ajax Amsterdam on four and Manchester City on two. Real visit Manchester on November 21 before hosting Ajax on December 4.
"If this is the toughest group and Real Madrid has always been in one of the two qualification spots then I don't know what the drama is," Mourinho said.
"If we get through this group it's an achievement and we are close to doing it."
Mourinho has a more immediate problem to deal with after Gonzalo Higuain was forced off at half-time on Tuesday, joining strike partner Karim Benzema on the injured list.
Neither were likely to be available for Sunday's La Liga match at Levante, Mourinho said, when Real will continue their bid to close the eight-point gap to leaders and arch rivals Barcelona after a poor start to their title defence.
