The 58-year-old labelled James Collins' mistake, that led to the Royals' goal, as a "basic error", while Brian McDermott insisted the "lucky break" was just swings and roundabouts
A mistake by James Collins gifted Pavel Pogrebnyak the only goal of the game after just five minutes, the Royals holding on thereafter for an important victory against the Hammers, something Allardyce labelled as a "basic error".
Vaz Te, meanwhile, came on as a substitute with just over 20 minutes left in the second period as the visitors searched for an equaliser, but when he was presented with a golden opportunity to level the scores with five minutes left he headed wide from six-yards out.
The east London side's boss rued the missed chance, which he labelled as "the easiest chance you will see", and says that you should not expect to get anything from a game if mistakes like that are made.
"James Collins makes a basic error, they take advantage, Vaz Te misses the chance," he told reporters. "The easiest chance you'll ever see in a Premier League football match and he misses it.
"He's got a free header in the six-yard box, three-yards out, inside the goal-mouth.
"You make those kinds of mistakes and you can't expect to get anything out of a game at this level."
The 58-year-old then suggested that the early goal stopped their opponents from playing attacking football, making them hard to break down, while he also bemoaned suspensions as the club try to avoid slipping down the table.
"Once [Reading] got the goal [they didn't] want to come out and play," he continued. "They wanted to sit in and protect the 1-0 that we gifted them.
"If it's not bad enough us losing it today, we get Kevin Nolan booked and James Collins booked right on the last day of their suspension term. We'll miss them for the Norwich game on Tuesday which is going to be a tough one.
"We're beginning to look down for first time of the season. We don't want to get dragged into [the relegation scrap] if we can help it."
On-loan Andy Carroll played no part in the fixture as the England international remains out with a knee injury, and though he confirmed that the forward will not be fit for the clash on New Year's Day, the former Blackburn manager insisted the forward will come good at Upton Park.
"We don't want to send him back, we want to get him fit and scoring goals for us because he's a magnificent centre forward," Allardyce added.
Royals boss Brian McDermott, on the other hand, was in a better mood after watching his team steal a victory in front of their own fans
"You've got to finish it," he said. "I know [Collins] has made a mistake but [Pogrebnyak has] a one-on-one and that's not an easy finish.
"They had the [chance] with Vaz Te where he headed it past the post, but having said that Jem Karacan had a shot that hit the bar so it's swings and roundabouts really. We got a break with the Vaz Te one, though."
The 51-year-old also suggested the newly-promoted side will be busy in the January transfer window, after being linked with players such as Arsenal's Andrei Arshavin, adding: "I think we're going to do some stuff."