The Championship promotion hopefuls took an early lead through Kevin Nolan but they failed to build on it, allowing James Coppinger's 73rd-minute strike to earn an unlikely 1-1 result for the Yorkshire side.
The point kept the Londoners ahead of third-placed Reading on goal difference but, with the Royals winning their last eight games, Allardyce knows that further slip-ups cannot be afforded if the Hammers are to achieve an automatic return to the Premier League.
He said: "Like the last couple of home games we couldn't finish the opposition off when we had the opportunity and then we become a little bit nervous.
"We should have won it at the death with Collision's effort 12 yards out but he put it wide. Chances like those are the difference between three points and one.
"We became a little nervous and lost our fluency allowing Doncaster back into the game. We had the golden chance at the end but we didn't take it and we are just not good enough at home at the moment."
West Ham have dropped 21 points in 18 home games this season.