The striker was sent off after tussling with Swansea defender Chico Flores during the Hammers' 2-0 win at Upton Park in the Premier League on Saturday.
However, replays showed that Chico played a part in Carroll's dismissal by over-reacting to the incident.
"Hopefully we get justice in Andy's decision being overturned," Noble told the club's official website.
"[Swansea boss] Michael Laudrup has come out on TV and said it wasn't a sending-off, so that's good honesty from the man."
West Ham continue their Premier League campaign on Saturday when they make the trip to Aston Villa.