With a 3-0 first-leg advantage, the Blancos looked like a firm favorite heading into Tuesday's game but Angel Di Maria's saved penalty and a first-half brace from Marco Reus made for some nervous moments.
Madrid survived more Dortmund pressure in the second period, with Henrikh Mkhitaryan striking a post while Iker Casillas was also called upon to make some crucial saves, and its coach confessed that his charges had almost paid for its poor second-leg showing.
"All games at this stage are very difficult," Ancelotti told reporters. "We are fortunate to be through to the semifinals. We're happy to reach the semis, but not happy as we suffered a lot, especially in the first half. We opened the tie up again.
"We were better in the second half. Football is like that, we gave away gifts, made lots of errors, we had no confidence and we suffered because of it. Casillas made fantastic saves in important moments of the game. His game was very, very good."