Villa currently sit 19th in the table and have struggled so far this season, also falling out of the Capital One Cup and FA Cup to lower league opposition.
One shining light for Paul Lambert's side has been summer acquisition Benteke who joined from Genk for a reported £7million fee.
The 22-year-old has already scored 10 league goals for Villa this campaign and Allardyce is aware that he poses the main threat to his West Ham side, who are looking to build on last weekend's win over Swansea.
"He's the biggest threat," Allardyce said of Benteke. "He's the man who scores the goals for Aston Villa on a regular basis, he's the focal point for their attacks in that he not only scores goals, but he holds the ball up, he's strong.
"He's had a fantastic start in what must have been a very disappointing season so far for Aston Villa. It says a lot for what he is as a player when he's producing what he is in a team that's been struggling for results."
Allardyce believes West Ham's poor away form, which has seen them score just seven times on the road and accrue only eight points away from Upton Park, means they cannot let Villa rush into a lead as they did in the 3-3 draw at Everton.
"The danger of Aston Villa is that if we allow them to get 3-1 up, I don't think we'll come back from that," he said.
"We can't afford that. Having the lowest goalscoring ratio away from home in the Premier League is why we haven't picked the results up.
"We can ill afford to let Aston Villa get off to the sort of start they did against Everton. We've got to avoid that at all costs and play our way into the game, making sure we don't give them any opportunities to score."