The European champions were beaten 2-1 on aggregate by city rivals Atletico Madrid in the Supercopa - with Friday's 1-0 defeat at the Vicente Calderon ultimately proving Real's undoing.
Luka Modric's dismissal compounded a difficult night for Ancelotti's charges, but they have little time to dwell on the loss as they begin their league campaign at the Santiago Bernabeu.
Real have not won the league since 2012 and were unable to take advantage of Barca's difficult campaign last time out as Atleti clinched their first title in 16 years.
While Ancelotti successfully delivered the Copa del Rey and La Decima to the Bernabeu faithful, the Italian will be under pressure to clinch La Liga this term, having completed the high-profile signings of Toni Kroos, James Rodriguez and Keylor Navas.
And the 55-year-old coach is confident that Real will not be knocked off course by the defeat to Atletico.
"The new season is going to be interesting for us," said Ancelotti, who has no fresh injury concerns ahead of Monday's clash.
"We have a side full of quality and we are going to try and do what we did last year. None of us have spoken about winning six titles.
"We will try and win all the titles we can. Now we start a new season and are looking forward to it. There are very competitive sides to come, like Atletico and Barcelona."
While Real begin their campaign with title ambitions, Cordoba make a return to the top flight for the first time in 42 years.
The visitors sealed their La Liga place in dramatic fashion in the second leg of the Segunda play-off final last term amid chaotic scenes and pitch invasions.
After a break in play, Cordoba got the away goal they needed against Las Palmas to ensure promotion but face a tough task at the Bernabeu despite Albert Ferrer bringing in the likes of Borja Garcia, Mike Havenaar and Jose Angel Crespo during the close-season.
Fidel is another new arrival at the club and the Elche loanee sees no reason why his new team-mates cannot cause a shock at the home of the 32-time Spanish champions.
"We're going to Madrid with all the enthusiasm in the world, with nothing to lose and to give the best image we possibly can," the 24-year-old said.
"Why can't we take something positive away from the match? You never know in football, there can always be surprises. We can give them a surprise in the first round."
