The European champions saw their lead at the top of La Liga lead cut to just two points after a 1-1 home draw against Villarreal last time out.
With Barcelona snapping at their heels, another slip-up could cost Real the league lead ahead of what is sure to be a crucial Clasico clash later this month.
"The team is improving - we've dropped two points [against Villarreal], but La Liga will be decided in the final match," Ancelotti told Real's official website.
"We have to focus on the two-point lead we've got, which isn't much, but is a lead we must make the most of.
"Now we have to carry on [against Athletic Bilbao] which will be difficult. [We will] try to produce a good reaction."
Real only need to look at their clash against Bilbao earlier this season for inspiration.
Star forward Cristiano Ronaldo scored a hat-trick on that occasion, while Karim Benzema added two in a comprehensive 5-0 thrashing.
And it would not surprise if a scorned Real side find plenty of joy in front of goal on this occasion.
Ancelotti has been boosted by Sami Khedira's return to training, but is still without James Rodriguez and Sergio Ramos.
The visitors will also enter the match fresher after Bilbao won through to the Copa del Rey final on Wednesday.
A 2-0 victory at Espanyol gave them a 3-1 aggregate success, setting up a May 29 final against Barcelona.
The win was Bilbao's second in a row, coming on the back of a 1-0 Liga success at Eibar.
They still sit 10th in the table, though, and have lost nine of their last 10 against Real - a statistic that will not fill them with confidence.
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