Ancelotti was not convinced by his team's performance after it was beaten 1-0 after extra time and won 4-2 on penalties away to its city rival.

The visitor conceded after 27 seconds to level the tie and make it 2-2, where the scores stayed until the penalty shoot-out.

But after Antonio Rudiger converted the winning kick, Real Madrid will face Arsenal in the quarter-final for a place in the final four.

"I have tried to explain to my players that the priority was not to make the game more complicated than it already was," Ancelotti said.

"We made it more difficult by losing unnecessary balls that constantly found us out of position... If they scored 2-0, then the game could have got out of control... We played better as the game progressed, had our chances, but we need to improve in our focus and concentration.

"We always have to look for improvement. The tie was evenly matched and a mistake could have been costly. We wanted to finish the game before penalties, sure, but here we are, still fighting and in contention, as is customary at this club." 

Jude Bellingham, meanwhile, scored one of Real Madrid's penalties in the shoot-out and acknowledged that both him and his team-mates had to dig deep to get over the line.

"That's sometimes what it takes, those moments of composure and poise. It's not always the mad quality that you see from us," the 21 year-old said. "There is a change of mentality when we come into these games, we know that there's a certain way of winning games.

"We're very good at that. We understand game situations really well, and tonight was another example."

Real Madrid had to rely on some good fortune during the tie, which did not resemble the performance it produced in its 6-3 aggregate victory over Manchester City.

Instead, after being stunned by Conor Gallagher's early strike, it was the beneficiaries of a huge slice of luck when Julian Alvarez's penalty was ruled out in the shoot-out.

The Argentine slipped when taking his spot-kick, which went in, but as he had inadvertently touched the ball twice, the VAR ruled it a miss.

Atleti goalkeeper Jan Oblak did save Lucas Vazquez's penalty, but a miss by Marcos Llorente allowed Rudiger to squeeze his decisive penalty in.

"Really happy. It's a huge game for us to win," Bellingham said. "It's massive for us, so important for us to get through at this stage. It will mean a lot to the fans because of who we were playing against."