The 30-year-old central midfielder did not come on as a substitute, as the match ended in a 1-1 draw.
The Hammers will return to action on Wednesday evening when they take on Everton away from home at Goodison Park in the Premier League.
West Ham boss Moyes has suggested that Noble is not guaranteed to start against Everton this week.
Moyes told Football.London when asked if Noble will be part of the West Ham team on Wednesday: “He will certainly be a part of the squad.
“We have quite a bit of competition for places but there is no problem in playing him if we need to because he is a good player.”
Noble has been at West Ham his entire professional club football career so far, but his performances in recent seasons have not been great.
A hard-working central midfielder, the 30-year-old is not playing well at the moment, and Moyes's comments will be worrying for him.
If West Ham do well without the Englishman, then he would find it hard to regain his place in the starting lineup.