The home fans were audibly frustrated by the Hammers' ineffective display in east London, where the controversial sending off of Allan McGregor arguably proved the difference.
The officials missed Mohamed Diame's handball before being taken down by the Hull goalkeeper, allowing Mark Noble to send home the resulting penalty.
The visitors managed to pull level early in the second half when Nikica Jelavic deflected home a Tom Huddlestone free-kick, only for a James Chester own goal to put West Ham back in front soon after.
Hull continued to press but were unable to stop West Ham running out unconvincing 2-1 victors - a performance that led to boos at the final whistle and Allardyce to react by cupping his ear.
"I've not experienced that before in the time I've been in the game," he said in the post-match press conference.
"Obviously, for us, today was all about coming off with three points, whether we played brilliantly, indifferently or not so good. It was about getting the three points
"The lads have gone about it and, when they've come off the field, they've got the three points and that is what matters.
"I have to remind everybody about the situation of playing against 10 men and the two examples of how difficult to beat 10 men.
"We were brilliant playing with 10 men when we beat Cardiff 2-0 and we played here against Swansea City for 65 minutes with 10 men and they didn't score and we won the game.
"Hull City played with 10 men, kept the ball well and we beat them. That's what you've got to do. The examples prove just how good we are. We beat them, that's the most important thing."
Asked about cupping his ear after the final whistle, Allardyce said: "I did it because I was hearing booing, I couldn't quite believe it.
"I'd seen something I've never seen before. Nothing surprises me, I suppose.
"I can't understand it, to be honest. We've got a difficult situation and it must be frustration."
Hull counterpart Steve Bruce joked about the full-time reception - "Sam's big and ugly enough to handle it" - but that could not disguise his anger at the officials' display.
The Tigers boss was furious with referee Mike Dean's decision to send off McGregor and called for changes to be made.
"If the referee had given the penalty straight away, I could understand," the Tigers boss said. "He didn't and we have got video evidence of that.
"I asked him if he gave the penalty and he said he did, but it must have been two or three minutes before he made the decision.
"So, if he has given the penalty, we obviously had someone on the line to clear the ball, so we must have some in line with him, so it's not really denying a goalscoring opportunity.
"And is it not sufficient to use common sense and, if he thinks it's a penalty, which he didn't at the time, keep 11 men on the pitch? I am convinced if we had 11 men we would take something from this game.
"With 10 men, for me, we were still the better team. With 11 that would obviously have been easier.
"McGregor obviously got injured and I honestly think that has made the decision for the referee, the fact he is in a bad way.
"But he has missed a blatant handball so it is a calamity of errors and what makes it worse is if he's not sure about the decision, then how does he send the player off?
"There is no more common sense. There are people marking them in the stands, they get paid handsomely and too often we're sitting here talking repeatedly - any manager I see - about a decision going against you.
"For me, it's too often. We've got to do something about it. They've got to improve."
As if defeat was not bad enough, Hull goalkeeper McGregor appears to have been seriously injured in that controversial incident.
"McGregor is in a bad way, kidney damage," Bruce said.
"A specialist is on his way to see him, it is a contusion on his kidney. We're hoping it's not ruptured. He's gone to hospital and he'll be staying overnight."