Allardyce's men won for the fifth time in eight matches after showing excellent resolve at The Hawthorns to come from behind for the three points.
Craig Dawson put West Brom in front in the 10th minute but the visitors hit back thanks to first-half goals from Kevin Nolan and James Tomkins.
West Ham then withstood a series of late home attacks to hold on for a win that keeps them fifth in the table.
Allardyce's jovial mood was summed up when he entered the press conference and joked: "We're going to win the league now."
He continued by saying: "Our summer months of hard work in recruiting terms, I suppose, and what we did in pre-season, is still paying off for us.
"Our strength in depth of the squad is what's paying off for us at the moment.
"We've had to change the team again, some by fatigue, some by an injury, and use the squad to use its maximum again.
"In the end, we've pulled off another victory. I'd say it wasn't great, particularly the second half, but it was resilient.
"We knew what we had to do and we did it.
"Having come back from 1-0 down, particularly away from home is always a big task."
Allardyce added that the second half did not please him, but it did not stop him from feeling positive.
"I was disappointed in the second half, I have to say," he added.
"I thought we were going to go on and create even more chances…but we defended right and defended well to secure the three points.
"Twenty-four points for us, at this stage of the season, is one hell of a total. If you look where we were at this time last year, we were almost in the bottom three, I think."
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