The Hammers are currently fourth in the Premier League, only seven points behind table toppers Chelsea, though Allardyce is wary of the expectation levels that come with such a lofty league position.
"It's not difficult for me but sometimes the players find it a bit difficult," he is quoted as saying by London24. "You play for the enjoyment and the praise that you get but make sure you manage it and control it well.
"I said to the players don't start reading about yourself too much or else we'll have to start changing the size of the doors to get your heads through. So keep your feet on the ground and don't read too much praise about yourself like you shouldn't read too much of the criticism.
"We have got to maintain it and our levels of performance. That is my responsibility because we have not been tested like this before and whether we can sustain this success."