Javier Hernandez scored the only goal of the tie two minutes from time after Atletico had been reduced to 10 men as Arda Turan was sent-off for two bookable offences.
It was the first time in eight meetings that Real had beaten Atletico this season, but Ancelotti dismissed suggestions they lack the firepower to compete with tournament favourites Bayern Munich and Barca.
"If we play with the desire we did today, Real Madrid can compete with anyone," said the Italian.
The holders were without injured Luka Modric, Gareth Bale and Karim Benzema, as well as the suspended Marcelo but Ancelotti is confident that at least Bale and Benzema could be fit for the semi-finals.
"We will recover the injured players for the semi-finals so the things are going to improve,” said Ancelotti. “I think Bale and Benzema will be fit quickly but I cannot say an exact day."
‘Juventus 'not afraid' as semi-final looms’
Juventus coach Massimiliano Allegri insists his side will not be in the Champions League semi-finals just to make up the numbers after the Italian giants edged past Monaco on Wednesday evening.
The Serie A leaders played out a 0-0 second-leg draw at the Stade Louis II to win their quarter-final tie 1-0 on aggregate, Arturo Vidal's penalty in Turin last week ultimately proving to be the difference.
While Juve have recovered from the Calciopoli scandal that rocked Italian football in 2006 to dominate again domestically in recent seasons, they have not been in the last four in Europe's elite club competition since 2003.
"We are not afraid. This was an important objective for us but not the final one,” said Allegri. "There would be no point in qualifying if we didn't want to go even further. We will of course look to reach the final."
In his first season in charge of Italy's most successful club, Allegri has Juve on the brink of retaining the Serie A title, in the final of the Italian Cup and now they remain in with a chance of continental glory, 30 years after they won their first European Cup on the night of the Heysel disaster.
Like Sports on Facebook, follow @ETribuneSports on Twitter to stay informed and join in the conversation.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ