Allardyce saw his team move 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 the three points against Norwich City.
West Ham have now taken 10 points from their last four top-flight outings, recording clean sheets in all those games, and have the breathing space of a four-point cushion on the relegation zone.
However, Allardyce is refusing to get ahead of himself, indicating after Tuesday's match at Upton Park that Premier League survival remains his primary objective.
"(It was) a hard-earned victory - Norwich gave us a fantastic game," he said.
"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, which has now kept 13 clean sheets in 26 Premier League games this term - the highest number of shut-outs in the division.
"Norwich had the better of the second half but when you're as good as we are defensively, then you've got to do that (defend well) then wait for the right opportunity," he added.
"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."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
