Allardyce furious with Nolan indiscipline
Nolan was shown a straight red card seven minutes from time when his side were 3-1 down for a reckless challenge on Jordan Henderson to compound a miserable afternoon for the struggling London club at Anfield.
The midfielder will now face a three-match ban, while winger Stewart Downing (foot) and defender James Tomkins (hamstring) were added to West Ham's lengthy injury list.
The Upton Park club are only out of the relegation zone due to their goal difference and manager Allardyce was furious that he will be unable to call on Nolan for the next three games.
He said: "We had to take James off because he felt his groin. It's getting massively concerning with the players losing their fitness.
"There is nothing we could do about Stewart's injury, but Kevin certainly could have done something about keeping himself on the field.
"It was a very irresponsible action. No matter how frustrated you get, you shouldn't be doing that sort of thing, especially when you're a man of his experience.
"We're all struggling at the minute, but what we can't afford to is lose our confidence and our determination to do the right things.
"It's not so long ago - a week - that we a magnificent performance together to beat Fulham. This time of year, the chances to put things right and win come thick and fast because the games come around and points are won and lost very quickly.
"My problem now lies with the limited amount of players I have available to me next weekend."