The big moment of Saturday's Premier League match came 12 minutes in when Robbie Brady went down under Joey O'Brien's challenge and won a penalty, which he dispatched.
West Ham were denied their own spot-kick when the ball struck Jake Livermore on the arm in the second half, and Allardyce was not pleased.
"I don't think you can create as many chances as that away from home, but finishing off is a big problem for us today," said Allardyce.
"But I think the ultimate failing away from home is turning our chances into goals and again that was our failing that cost us getting something out of the game, irrespective of the referee's poor decisions.
"He has given two really poor decisions, two penalty decisions - but we should still have got something out of the game and that is the disappointing thing. It has happened at Newcastle, at Southampton and again here today and it is their responsibility to be more clinical in front of goal."
Allardyce believes his side were denied by Friend over the two penalty decisions and he believes Brady used 'simulation' to win the spot kick.
"They are major decisions. Brady takes a simulation on a slight contact with Joey O'Brien when the ball is not going near him and he buys the penalty and the referee falls for it," he continued.
"And Livermore puts his arm out for a corner but the referee doesn't see it and doesn't give us a penalty - it's our responsibility for not finishing chances, and the referee is responsible too for losing us the game."
Allardyce admitted he had talked to the officials, adding: "That is between him and me, now it goes through the delegate and seeing what they think and I will be following that up."
Allardyce insists that his side could and should have got something from the game and he refused to blame their tactics, despite the fact they have failed to score away from home this season.
"The bottom line is not as if we have gone away and not created chances," he said. "We have gone away and created numerous chances, but for whatever reason at the moment, they are not going in the back of the net."
He feels not getting something at Hull is a huge blow given their next two games are against Tottenham and Manchester City.
"We needed to get something out of the game and pick up more points," he said.
"You always try to pick up at least one point per game and now we have fallen behind - six games, and only five points. Two big games come now against Tottenham and Manchester City - but none bigger than this.
"If we play well today, we get something out of it. We could play our very best in the next two games and not get anything but we have to take it on the chin and try and get something out of the games against Spurs and Manchester City."