Defeats to the likes of Chelsea and Arsenal in recent weeks came about despite solid displays, with West Ham's early-season form having been somewhat undone by the disappointing run.
That sequence looked set to be extended against struggling Sunderland until Diafra Sakho's late winner proved the difference at Upton Park.
"It's nice to get a win and secure it just at the end," Allardyce said.
"Most of our failings over the past 10 or 11 games have been not being able to keep a clean sheet from a winning position.
"We've done that and even though the game was a bit scrappy, we deserved to win.
"Hopefully we can win more games than we lose or draw and we can push on and try finish as high as we can.
"The performances are there, the results are not. We just haven't been able to find the result we deserved.
"For us, it's a massive win. We're in a great position, we've 42 points and we're heading for probably the best points total since we got back into the Premier League.
"If anyone wants more than that, I really don't know how they can ask for more."
