But after introducing
And Mourinho was particularly happy with how the Spanish champion adapted to not having a recognised striker for 45 minutes.
The Real boss said: "We were losing and lost Higuain to an injury. We didn't have another centre-forward on the bench so we had to use four forwards with a lot of movement and a change of positions.
"Because we were playing with four forwards we also had to change Essien for Modric to have two players based in the midfield to pressure further forward.
"We made two huge defensive errors in the first half and, as is normal when you play against the big teams, they kill you and don't miss chances.
"They had too much time on the ball without pressure in the first half but in the second it was completely different. The team was quick, dynamic and aggressive and I liked it a lot."
Mourinho was also relaxed about the possibility that Real could now finish the group in second place and face in theory a tougher tie against a group winner in the last 16.
"If the group finishes now we are qualified. This is the toughest group and to qualify from this group is a success," he added.
"If we finish second it is a problem for the other teams that finish first in their groups. If you finish first you expect to play an easier rival but they could play Real Madrid.
"If I were a fan I would prefer to see a game like this and draw than the games in other groups which are like Europa League games.
"The two times I have won the Champions League with Porto and Inter Milan I have finished second in the group.
"We will obviously try to finish first and get the maximum points possible."
"It is relatively difficult to plan a game against Real Madrid beforehand," he said.
"We were clear we had to do the same as in the first game but the difference is when you play in
"Our plan was not to make those mistakes to have good control of the ball and I believe we have achieved this.
"We have played very well but after the break Real came back stronger we couldn't react as well to the changes and that was key.
"A draw is still a very good result. We knew it was going to be very hard and sometimes you need to be lucky.
"We have direct qualification in our hands, but there are still two games to go."
Klopp was also quick to calm suggestions that Dortmund could now challenge to win the Champions League this season and pointed out that just reaching the last 16 would be unchartered territory for his young side.
"In the last two years we have gained experience," he added.
"It is clear we have to go forward and we know this group is very difficult but we have never been in the last 16 of the Champions League or the Europa League so it will be a big success to reach this round.
"However, if we reach this stage we will obviously do everything in our power to reach the quarter-finals."
Borussia Dortmund has confirmed Mario Gotze will miss the Champions League final against Bayern Munich at Wembley on Sunday (AEST).