Everton will be without midfielder James McCarthy for up to three weeks while goalkeeper Maarten Stekelenburg is unlikely to recover in time for Monday's Premier League trip to Leicester City.
Ireland international McCarthy was withdrawn with a hamstring injury during Everton's 1-0 defeat by Liverpool last Monday, while Dutchman Stekelenburg hurt his leg in a collision with team mate Leighton Baines and also had to be replaced.
"I think Maarten Stekelenburg will be doubtful for Boxing Day and James McCarthy is out with a slight hamstring (injury) and that's bad news because he was doing well," manager Ronald Koeman told a news conference on Thursday.
"I am worried because of his many muscle problems but I think he can be back in two or three weeks."
Everton are ninth in the table with six wins from 17 games and the Dutchman pointed to champions Leicester City's struggles this season as proof of how competitive the Premier League is.
Leicester are in 15th place, three points above the relegation zone, but have fared better in the Champions League, qualifying for the last 16 as group winners.
"I think we can't find a better example (than Leicester) of how difficult it is in the Premier League. They evolve in the Champions League, of course, but it's not the same Premier League season for them. That's normal."
Koeman has already asked for time to rebuild his squad and turn around Everton's fortunes and reiterated the message in the wake of the Merseyside derby defeat.
"We know it's a difficult time, but I knew that before," he said. "I wasn't expecting good results every day. We know what we need to do to improve and that is not done in two months."
The Dutchman, who caused a furore among fans earlier in the season by suggesting striker Romelu Lukaku would have to leave the club to fulfil his potential, also said Everton were in talks with the player's agent over a new contract.
"I know that they are in talks together about a new contract," he added. "If it's 90 percent, 99 percent, I need to believe his agent.
"In football you don't know what can happen in one year but at least there is understanding and the boy likes to stay. He's a big part of the Everton future."
(Reporting by Simon Jennings in Benglauru; editing by Ken Ferris)