The 32-year-old France international was substituted after 33 minutes in the second-round clash on Tuesday and scans have revealed the damage to be worse than originally feared.
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"Our team news is that only Alou Diarra, who unfortunately got injured the other night, is not involved in the squad," the Hammers boss confirmed ahead of West Ham's Premier League meeting with Stoke City on Saturday.
"The injury is more serious than we expected and it's an ACL reconstruction, it looks like, so that will almost certainly finish Alou's season.
"It's a big blow to us in squad terms - he was hoping to force his way into the side this season but, obviously, after that injury that now won't be the case."
Midfielder Diarra still has two years left of the three-year contract that he signed in 2012.