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.
City 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," Allardyce told reporters.
"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."
Despite having the personnel advantage following McGregor's red card, Allardyce offered a reminder of their successes with 10 men.
"I have to remind everybody about the situation of playing against 10 men and the two examples of how difficult it is to beat 10 men," he added.
"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."