The Hammers have made an excellent start to life back in the top flight following promotion last season, and currently sit comfortably in the top half of the Premier League.
That lofty position could be affected in the coming weeks, however, by the trip to Manchester United to come before home clashes against the likes of Chelsea and Liverpool, and Allardyce is fully aware of the difficult challenge lying ahead for his side.
"I think that the players at this football club worked very hard last year to play in fixtures like the ones coming up," he told reporters.
|28/1||West Ham are 28/1 with William Hill to beat Man United 1-0 on Wednesday|
"It is always a massive challenge for a newly-promoted side to face the likes of Manchester United but I think it is a challenge that the players look forward to.
"It is all about accumulating the points and continuing to pick them up as often as possible. If we carry on to do this then we will move towards a points total that will ensure safety."