The Hammers have not won in the league since the 2-0 victory over Cardiff on the opening day of the season.
Allardyce had been banking on Hull for three points but his side suffered a narrow defeat at the KC Stadium.
Things are unlikely to get easier any time soon, with a trip to Tottenham and a home clash with Manchester City coming up either side of the international break.
And Allardyce has already accepted that even full-power performances from his side may not be enough to take anything from that big-hitting pair.
"It's worrying, yes. We haven't got anything out of the game when we needed to get something," said Allardyce after Saturday's 1-0 loss.
"You're always trying to stay ahead of points per game and now we're falling behind.
"We have played six games for five points and have two big games against Tottenham and Manchester City coming up, but none bigger than this one, as I told the players.
"The next two are not as big as this was which was one where, if we play well, we can get something out of. We played well but didn't finish properly.
"We can play at our very, very best in the next two and get beaten. But we have to take it on the chin and try and get something from the next two