The 26-year-old Pickford, who has made seven errors directly leading to goals in the Premier League since the start of last season, was guilty of another erratic showing in Sunday's 3-0 defeat by Wolverhampton Wanderers.
"I don't know if he needs competition. I know that he's not doing well. I spoke to him about this. He has to be focused on himself, on his performance, day by day to try to be better," Ancelotti told reporters.
"I'm not so worried because he has quality, character, but I have to say to him and I've said to him, that he has to improve. I have, and everyone else at the club have, total confidence in his quality.
"He can do better and he knows this because he is critical of himself. I hope there is improvement in the next games ... for the quality that he has, and he agreed, he has to be better."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Robert Birsel)