Rice and Grealish, who both snubbed Ireland to represent England, scored in the first half of Carsley’s maiden game in charge following Gareth Southgate’s exit.
Southgate quit after England’s heartbreaking Euro 2024 final defeat against Spain in July.
Carsley, who guided England Under-21s to European Championship glory last year, has stepped up on a temporary basis while the Football Association seek a permanent successor to Southgate.
Newcastle boss Eddie Howe and former Chelsea manager Graham Potter are said to be among the leading contenders.
But Carsley’s hopes of landing the job himself were boosted by England’s confident display in the Nations League Group B2 victory at the Aviva Stadium.
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