Madrid just needed to avoid a defeat to go through to the knockout phase as group winners, but they ultimately battled to a commendable victory over the Italian champions.
Toni Kroos netted a glorious first-half opener, before a similarly satisfying Marco Asensio curler wrapped up the win 11 minutes from time.
As such, Madrid will – theoretically – get a kinder draw than runners-up Inter in the last 16, potentially setting them up nicely to reach the quarter-finals.
Los Blancos went as far as the last four in 2020-2021 following back-to-back round-of-16 eliminations, though Ancelotti is not making any sweeping statements regarding their chances of going deeper into the competition this time around.
He said: "We have the quality to win LaLiga and the quality to compete in the Champions League.
"There are no teams with the quality [guaranteed] to win the Champions League, just to compete.
"There are more intense teams, others with more quality. We are not an intense team in the defensive aspect, but we have a lot of quality, a lot of experience and a lot of commitment."
Luka Modric made his 100th Champions League appearance on Tuesday, becoming only the ninth player to reach that landmark while at Madrid. Eight of those games came during his time at Tottenham.
Modric turned in a typically controlling display and completed the full 90 minutes, which was somewhat surprising given the important nature of Sunday's clash with Atletico Madrid.
There had been calls prior to the weekend win over Real Sociedad for Ancelotti to rotate his midfield more, yet Modric is heading into the derby having played 90 minutes both against La Real and Inter.
The Croatian is not concerned, however.
"I feel very good," the 36-year-old told Movistar. "I think you don't have to look at the years, you have to look at what you do on the field. The years are less and less noticeable because players' careers are prolonged.
"I feel very good, and I feel like I am younger than 30!"