Real appeared lost without injured top scorer Cristiano Ronaldo, who watched anxiously from the bench as the La Liga giants were comprehensively outplayed in a 2-0 reverse in the quarter-final, second leg that meant they squeaked into the last four 3-2 on aggregate.
Both of Marco Reus’s goals for Dortmund came after Real howlers, the first when centre back Pepe headed the ball into his path in the 24th minute and the second when midfielder Asier Illarramendi surrendered possession.
The Bundesliga side, who knocked Real out in the semi-finals last season, came close to levelling the tie when Henrikh Mkhitaryan’s shot hit the post in the 65th minute but Real held out and will go into Friday’s draw for the last four as they chase a record-extending 10th European crown.
They are third in La Liga, three points behind leaders Atletico Madrid with six games left, and also through to next Wednesday’s King’s Cup final to face arch rivals Barcelona.
Barca are the only Spanish side to have won the Champions League, La Liga and the King’s Cup in one season, in 2009 under Pep Guardiola.
A relieved Ancelotti said the match in Dortmund had turned when Angel Di Maria’s 17th-minute penalty was saved by home goalkeeper and captain Roman Weidenfeller.
“We gifted them a lot, above all in the first half,” the Italian, who has 39 wins, six draws and five defeats in his first 50 Real games, told a news conference.
“In the second we didn’t lose our heads, we defended better and we had chances to score,” he added.
“I am pleased to get to the semi-finals, which was an important goal, but not with the way which we did it.”
PENALTY MISS KEY
Real’s lethargic and error-strewn performance almost wrecked their chances of a fourth consecutive appearance in the semi-finals of Europe’s elite club competition and they will have to improve if they are to reach next month’s final in Lisbon.
“The key was the penalty, which gave Borussia a big lift, and at that moment an element of fear affected the team,” Ancelotti said.
“We didn’t play after that moment and only defended. We needed to have control of the game and possession and in the first half we didn’t manage it.”
Chelsea, coached by Ancelotti’s predecessor Jose Mourinho, are also through to the last four and Real’s other possible opponents are La Liga rivals Barca and Atletico, holders Bayern Munich or Manchester United.
Ronaldo, top scorer in both La Liga and the Champions League this season, should be fit for Saturday’s game at home to Almeria, Ancelotti said.
The Portugal forward, who has a record-equalling 14 Champions League goals in the latest edition, has been undergoing treatment for a left knee problem and Real decided not to risk him in Dortmund.
(Editing by John O’Brien)