West Ham have won five of their opening 11 league games and are six points better off than their opponents.
"When you continue to get results, then people can't ignore what you're doing, both as a manager and a group of players and coaching staff," admitted Allardyce.
"Most of us have been here (in the Premier League) before - certainly I have for a long time and we know the position we're in is a very good one.
"But we know only a quarter of the season has gone. It's a great start and that's all it is."