The Hammers have won just once since the opening day of the season and are only above the relegation zone on goal difference.
Nolan said: "We just need the fans to stick with us because they have been fantastic for us.
"We apologise for this result and I firmly believe we'll still be in the Premier League with them at the end of the season.
"We're under no illusions, that was a very disappointing result. We've got to take it on the chin - whatever anyone wants to throw at us, write or say about us now, we've got to take it as a squad.
"It's a long old season but we know we've got to turn it around pretty soon otherwise we're going to be in a dog-scrap come the end of the season."
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