The Italian coach was relieved his team could edge past Dortmund to the Champions League semi-finals despite a 2-0 second-leg loss, while Jurgen Klopp praised his beaten players
With a 3-0 first-leg advantage, Los Blancos looked firm favourites heading into Tuesday's game at Signal Iduna Park, but Angel Di Maria's saved penalty and a first-half brace from Marco Reus set Madrid nerves jangling.
Madrid survived more Dortmund pressure in the second period, with Henrikh Mkhitaryan striking a post while Iker Casillas forced into making some crucial saves - and the Italian coach confessed that his charges had almost paid for their poor second-leg showing.
"All games at this stage are very difficult," Ancelotti told reporters. "We are fortunate to be through to the semi-finals.
"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."
Jurgen Klopp hailed his BVB side as "incredible" after their impressive display, insisting his side were the better team after coming so close to levelling the tie on the night.
"Neven Subotic said to me after the game, 'I couldn't be prouder of this team'," Klopp told reporters.
"That's what the Champions League is about. We were superior tonight, but should have scored last week.
"Tonight's game was so good that there is absolutely no-one to blame for not qualifying.
"The atmosphere was awesome. We wanted to prove a point and we did that with our incredible performance."
Bayern Munich or Manchester United and Atletico Madrid or Barcelona, who play on Wednesday, will join Real Madrid and Chelsea in the last four of the competition.
Love Champions League football? Then you’ll love the great DVDs on offer at Goal’s Official DVD Store – click here to take a look!