The 58-year-old has guided newly-promoted West Ham to seventh following the first 12 league games of the campaign but his side are currently in the midst of a difficult run of fixtures. After facing champions Manchester City and travelling to Newcastle, Allardyce's side now face Tottenham on Sunday with a trip to Manchester United on Wednesday.
"We know we are in a very good position but this run of fixtures could cause us a few problems," he said.
"I think we will play well and I do not think we will let ourselves down but we could play our best in the next four games and lose all four."
The Hammers will also meet Chelsea, West Brom, Everton and Arsenal - the four sides directly above them in the table - before the turn of the year with Allardyce all too aware of the ability of their upcoming opposition.
But despite the difficult run Allardyce has backed his players to continue their decent start in the type of fixture they yearned for during last year's successful npower Championship season.
"I think that the players at this football club worked very hard last year to play in fixtures like the ones coming up," he said. "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."
West Ham missed out on the chance to move up to fifth in the table after being held to a 1-1 draw by Stoke on Monday night. Since that result the club have been linked with a move for former England captain David Beckham, who has confirmed he will leave LA Galaxy following next month's MLS Cup final.
However Allardyce reckons it would be difficult to persuade Beckham to move to any English side other than Manchester United, where the 37-year-old collected six Premier League trophies and a Champions League winners medal amongst many other honours.
"David has always said to me when he has been available that he only wanted to play for Manchester United in this country and I haven't heard him say he wants to come back to England," he said. "It is speculation until David decides where he wants to go. I am not so sure about the situation at all."