Allardyce delighted with clean-sheet victory
The hosts were a touch fortunate to go ahead early on, as Enner Valencia was guilty of handball before Nedum Onuoha turned a Stewart Downing corner into his own net.
However, West Ham were the better team at Upton Park and climbed to seventh in the Premier League table after Diafra Sakho struck for the fifth time in as many starts with a second-half header.
"I think that we were very comfortable, except perhaps for 10 minutes into the second half when they changed their system and we didn't really come to terms with it," Allardyce told Sky Sports.
"That gave us a little bit of a problem for a while, but when the second goal came, it settled us down again and got us back into our rhythm.
"If I was to have a little bit of a criticism, it would be for not punishing them enough with the amount of times we were in or around the final third.
"Perhaps we could have done a little better with those opportunities, but that's being ultra greedy on the basis that we've won very comfortably and kept a clean sheet, which is what I've been striving for, because you can't score two or three goals every game to win.
"But this time, we've scored two, kept a clean sheet and it's a perfect result for us."
Downing was also singled out for praise, with the manager stating: "He's started to get a bit of confidence back and when you've got the amount of talent and ability he has, you've got everything to be a major influence."