Foden, Palmer and Watkins ruled out of England's Nations League games
England face the Republic of Ireland in Dublin on Saturday before hosting Finland at Wembley three days later in League B.
Chelsea star Palmer, who scored in England's Euro 2024 final loss to Spain, and Aston Villa striker Watkins have returned to their clubs with injuries.
Manchester City forward Foden did not join up with Carsley's squad due to illness.
"No further additions are planned at this moment in time," the association said in a statement.
The match against Ireland will be England's first since Gareth Southgate's eight-year reign as manager ended.
Carsley has been placed in temporary charge and he has given Noni Madueke, Morgan Gibbs-White, Tino Livramento and Angel Gomes their first call-ups.