The Republic of Ireland international won a first-half penalty when he went down under a challenge from Joey O'Brien and then added further to Allardyce's ire by stepping up to put away his fourth of the season.
Allardyce felt the former Manchester United junior had influenced referee Kevin Friend by going down too easily as O'Brien put his hands on him and was not afraid to say so afterwards.
He also told his own players they were responsible for the loss too - poor finishing their greatest crime - while another decision not to give a second penalty for an alleged handball by Jake Livermore also got his back up.
"Not finishing off our chances was a big problem for us," he said.
"The ultimate failing we have away from home is not turning our chances into goals.
"Again that cost us something out of the game, irrespective of the two poor decisions the referee has given. There were two really poor decisions, but we still should have got something by capitalising on the chances we created.
"That's the disappointing thing for me and is a massive problem for the players and their responsibility to be clinical."
On Friend he added: "The other side is two very poor decisions in terms of major decisions by the referee. One, Brady takes a simulation on a slight contact with Joey O'Brien when the ball is not near him or the goal. He buys the penalty and the referee falls for it.
"Livermore puts his arm out and knocks the ball for a corner but the referee doesn't see it and doesn't give us a penalty. So it's our responsibility for not finishing our chances and the referees as well for us losing the game."
The remaining narrative of Allardyce's assessment was centred on his side's anaemic final-third play.
They have failed to win in the Premier League since the opening day as a consequence of it and have five points from six games.
"It's a worrying trend but it's not as if we've gone away from home and not created chances," he said.
Hull manager Steve Bruce has no such worries.
Since an opening-day chasing at Chelsea his side have accrued 10 points as a result of carrying over their dogged displays from the Championship last season.
Even then they relied on a lot of narrow wins, like this one, but their defence was their hallmark and so it proved today as they muscled up to keep the Hammers out.
That Liam Rosenior left the field with blood pouring from his face was typical of their attitude.
"I couldn't be more pleased. The big decisions have maybe gone our way but you can't mask that we created the better chances," said Bruce.
"Their goalkeeper made more saves than mine, we hit the bar, the post but the talking point is the two decisions that went our way," added Bruce, who was not willing to engage in a war of words with his opposite number.
"I have seen the handball from Jake Livermore four or five times and can't see if it was deliberate or it hit him.
"From where the ref was standing and the linesman, they can't give it. The pen, I've not seen it yet. We might have got the decisions but were still the better side on the day."
Away from the furore of whether he dived or not, Brady is making a real impact on Hull's season.
The left-footer has been something of a surprise package so far and his manager is even more pleased considering he is playing with a problem.
"He's got a stomach problem which is causing us concern," Bruce said.
"Considering he has a problem, it's admirable that he keeps wanting to play. We might have to look at how long we can go for without surgery.
"But players like him, Stephen Quinn, Rosenior and George Boyd (Championship survivors) are enjoying trying to be Premier League players. We know how difficult the next six months will be, but we will make the best fist of it we can."