The midfielder was forced off after appearing to twist his ankle in the fourth minute of extra time at Old Trafford, and was replaced by Phil Jones.
Moyes was asked about Carrick's condition at the end of his post-match press conference. He replied, "I don't know [at the moment], I think he twisted his ankle."
The manager admitted that the 32 year-old may well have taken one of United's penalties in the shoot out had he still been on the pitch at the end of the 120 minutes.
"It probably wasn't the group of players we would have [ideally] chosen to take penalties," said Moyes. "Chicharito would have probably taken a penalty but he was injured. People like Michael Carrick would have been involved if he'd still been on the pitch. We didn't execute our penalties well enough."