A starter in the Eagles’ opening two games, the midfielder was a conspicuous absentee from the matchday three 2-1 home loss at Selhurst Park.
"Unfortunately, he picked up a slight strain. We were hoping he’d recover in time but we will have to do without him today,” Hodgson explained after Saturday’s tie, as reported by his club’s official website.
Saturday’s revelation about Schlupp’s fitness comes just a day after he was named in a 23-man Ghana squad for an international friendly against Mali in October, his call-up marking an end to an 18-month absence from national duty.
In his absence for the Premier League tie, summer signing Eberechi Eze took the 27-year-old’s place in Palace’s line-up.
"He [Eze] has done well since he has come into the club. His training has been impressive," Hodgson said, “but of course Jeffrey Schlupp has had that position [left-midfield] nailed down basically through the good work he did in pre-season."
Dominic Calvert-Lewin opened the scoring for visiting Everton in the 10th minute before Cheikhou Kouyate found the back of the net to level things at Selhurst Park.
Five minutes prior to full-time, Brazil attacker Richarlison converted a penalty for the away side to seal a 2-1 triumph on the road.
"I thought we started slowly and got ourselves back into the game well. And going towards half-time we were establishing some sort of control of the game,” added Hodgson.
"In particular, the second half, I thought the way the players got over the disappointment of finding themselves two goals to one down, in a way they felt was very harsh, and the way they approached the second-half was very positive.
"There were lots of very good individual performances and I would count Eberechi’s as one of those.”
Fifth on the league standings, Palace will hope to bounce back when they face Chelsea in their next game on Saturday.