The Londoners have won 2-0 in each of their last three Premier League games and risen to 10th in the table but the Hammers boss remains concerned about their proximity to the drop
The Hammers up to 10th in the table with their third straight 2-0 win on Tuesday, as late goals from James Collins and Mohamed Diame were enough to secure three points against Norwich City.
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"[It was] a hard-earned victory - Norwich gave us a fantastic game," he told reporters. "Late on in the game, we produced what we needed to. [It was] an outstanding victory for us.
"We're absolutely delighted we've got three wins on the trot, [it's] a terrific run of form we're in, [but] we're still not out of the bottom end in terms of the distance in points, [which is] still not that great."
Allardyce went on to pay tribute to his rock-solid defence, having now kept 13 clean sheets in 26 Premier League games this season - the highest number in the division.
He continued: "Norwich had the better of the second half but, when you're as good as we are defensively, then you've got to [defend well] then wait for the right opportunity.
"Now we're in a scoring mood and, because we're brilliant at keeping clean sheets, that's picking us up win after win after win."