The Hammers dominated possession at the Madejski Stadium and registered 13 shots - 10 more than their opponents.
"We shot ourselves in the foot from the early stages," Allardyce told BBC Sport. "James Collins has been solid for us this season but he made a basic error and they took full advantage.
"Reading defended deep in numbers and [Ricardo] Vaz [Te] has missed a glaring, glaring chance and two errors mean we have not taken any points against them.
"We are bitterly disappointed not to come away with a point and now we are without James [Collins] and Kevin [Nolan] through suspension for an important game against Norwich."
West Ham, who currently sit 12th in the Premier League table, have now taken just one point from their last four games.