I suppose I'm a bit of a masochist: I just re-watched the last 15 minutes of regular time, mostly because some of the post-match Twitter commentary was that Atletico slowed down the pace too much after scoring the tying goal in the 79th minute.
I presume that Atletico's players were gassed after the goal, and that Simeone did not want to allow a last-minute Real Madrid goal. As a result, Simeone seems to have reverted to his counter-attacking, defend-at-all-cost style -- the defensive line shifts back and Atletico stops pressing with the same intensity. Hindsight is, of course, 20/20, but Atletico should have kept the foot on the gas and gone for the match in the last 15 minutes of the game. I think Simeone should have attempted to have used the momentum to go for the goal, and to use the enthusiasm his players had to stay on top of Real Madrid. I don't think sitting back was the right decision in this case (in contrast, sitting back against Barcelona or Bayern over two legs makes sense).
Edit: In nearly the last breath of the match, Saul commits a foolish foul against Bale, giving Real Madrid a free kick. It goes nowhere, and it allows Atletico to counter. Carrasco, the goal scorer, was about one step too slow in trying to break free from Ramos. Torres or Griezmann may have not scored, but Atletico was damn close to having a chance to win at the last second in a three-on-one break.