The Hammers head into their final match at home to relegated Reading having already secured top-flight status after an impressive first campaign back up under Allardyce, who has recently signed a new two-year contract.
However, more tough challenges await the east London club as they look to become established in the Premier League ahead of their move to the Olympic Stadium.
West Ham are expected to be busy over the summer, and have already been linked with moves for the likes of Celtic forward Gary Hooper and Vitesse Arnhem's Wilfried Bony, top scorer in the Dutch league as well as veteran Italian midfielder Massimo Ambrosini, who is out of contract at AC Milan.
Allardyce accepts no matter how hard clubs might work to improve the squad, the additional financial outlay does not always correlate directly to more consistent results.
"For the small improvement, it is a considerable amount of millions which is needed today, that is the difficulty we all face," Allardyce said on talkSPORT.
"You buy a £10million player or a £12million player today and everybody expects the team to improve by 15 or 20 per cent, but often it is only by one or two per cent.
"The size of the fees for players and wages just don't relate to how much they improve the team.
"That brings more and more pressure on you as a manager in trying to improve the side.... but the money needed today is astronomical."