The Hammers have proven one of the surprise packages of the Premier League campaign thus far as Allardyce's troops sit fourth in the table, one point behind Manchester City.
West Ham have won four of their last five games - including home wins over City and Liverpool - but the veteran manager says that negotiating the next few months might prove their sternest challenge yet.
"We are on a big high at the moment, it is a fantastic feeling, but we are only nine games in and there is a long way to go yet," Allardyce told Sky Sports News. "We still have the difficult time ahead - it will be the end of November and December when all the games come flooding thick and fast.
"The new players - will they fatigue or won't they? We are absolutely delighted they have all hit the ground running, but they have never experienced this level of physicality.
"They could easily fall into December finding life extremely difficult, the rest of the squad may have to dip in then and help them out while we give them a rest. Hopefully it is not the case, but I have to be wary of that."
The East Londoners face tricky encounters with Chelsea and Arsenal in the space of two days after Christmas.