The champions trail Barcelona by three points at the top of the table and were soundly beaten by their rivals in the Spanish Super Cup final last week.
However they produced a sensational comeback from two goals down to beat Villarreal in the Spanish Cup on Thursday night, which should boost their morale.
Madrid's defence has been leaky, conceding eight goals in their last four games.
In La Liga, Madrid have let in 16 goals, 10 more than leaders Barcelona.
"We have conceded six goals (in three games) and five of them could have been avoided with a little more defensive caution," Ancelotti told reporters on Wednesday, before the Villarreal cup clash.
German international centre-back Antonio Rudiger has endured a rough ride since joining from Chelsea in the summer, and the defence has not looked close to its best all season.
Only goalkeeper Thibaut Courtois has been playing well, despite being able to keep just three clean sheets in La Liga from 16 matches.
Madrid have been hamstrung recently by David Alaba and Aurelien Tchouameni's injuries, meaning Toni Kroos has been forced to play as the deepest midfielder.
Ancelotti said January was proving tough for his team and they had to survive it before picking themselves up later on.
"We've had injuries that affected us a bit more and it was not foreseeable," said Ancelotti.
"Not being at our best is normal, we have to bear out this month."
Despite Madrid's form, Ancelotti was positive about the club's direction, saying they are starting a new era, rather than ending an old one.
"We've got a young team," said the Italian coach.
"They all talk about (Luka) Modric, Kroos, (Karim) Benzema, but we must also talk about the youngsters. Vinicius, (Eduardo) Camavinga, Rodrygo, (Fede) Valverde, (Eder) Militao, Tchouameni and players who are going to join in the future.
"I think this is the beginning of a new era. The players who have defined an era at this club are coming to the end of their careers, but there are others coming in."
Former Barcelona coach Ernesto Valverde will be looking to do his old side a favour at the San Mames, just as Villarreal's Quique Setien did earlier in January.
Athletic lost at local rivals Real Sociedad in the Basque derby last weekend so bouncing back against Madrid would be the perfect response.
Despite a dip in form which has seen Los Leones win just one of their last five league games, Athletic sit eighth and just two points behind fourth-place Atletico Madrid.
With Ancelotti's side looking defensively vulnerable, Athletic will view this match as an opportunity -- although Madrid's cup comeback is a warning they can never be counted out.
Player to watch: Izi Palazon
Rayo Vallecano's strong campaign to date is partly down to the spectacular form of winger Izi Palazon. With three goals and two assists in his last seven league matches, the Spanish forward has been key for the Madrid side, and if they are to get a result against high-flying Real Sociedad, Palazon will be crucial.
2 - Rayo's Ivan Balliu has the unfortunate accolade of being the only player to score two own goals this season
6 - Barcelona's strong form has been built on their rearguard, which has only shipped six goals this season in La Liga
36 - Espanyol midfielder Vinicius Souza has won more tackles than any other player in the league
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