The England international striker was controversially given his marching orders by referee Howard Webb in the game on February 1, after the official deemed he struck opposition defender Chico Flores with his arm.
West Ham saw an initial appeal rejected by the FA, before an independent tribunal upheld that ruling on Friday.
Carroll subsequently served the first game of his three-match ban in the club's 2-0 victory at Aston Villa on Saturday.
And Nolan - who scored both goals in that fixture to add to his brace against Swansea - believes his team-mate has been the victim of an "injustice".
"We have nothing against the FA, they've just got to get it right," the 31-year-old said.
"When people get things wrong, we expect them to hold up their hands and say, 'yeah, I got it wrong' and move on, like we all have to do.
"We have to hold our hands up as footballers when we get it wrong and take the stick that comes with it. I think they had a chance to redeem themselves and they haven't taken it.
"We were disappointed with the outcome. We thought it was an injustice. Andy is also frustrated, he's a good mate of mine and I felt really sorry for him.
"We've got to forget about Andy for the next couple of weeks now. He has to work hard and get himself ready because if we keep winning games it's going to be hard for him to get back into the team."
West Ham have taken seven points from their last three Premier League outings and now sit in 15th place, two points clear of the relegation zone, ahead of their home clash with Norwich City on Tuesday.
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
