The 18-year-old was substituted in the 24th minute of the second round encounter and, with fellow defender Mason Holgate also out injured, Italian Ancelotti has only two fit senior centre backs in Yerry Mina and Michael Keane.
"Holgate is out and Jarrad we don't know his injury and how bad it is, we have to look," Ancelotti told reporters.
"There is a possibility to find a centre back and I think we have to.
"The Holgate update is that he doesn't need the surgery so maybe he can recover earlier than normal, but I think we can manage until Mason comes back with three centre-backs no problem," he added.
Media reports said Everton were targeting a loan move for Chelsea's Fikayo Tomori before the transfer window shuts on Oct. 5.
Everton, who beat Tottenham Hotspur 1-0 in their Premier League opener, host West Bromwich Albion on Saturday. (Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford )