Having won four Premier League games on the trot in February, the Hammers have lost three in March to drop to 14th in the table, just six points clear on the bottom three.
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"We've put ourselves in a little bit of danger again, there's no doubt about that," Allardyce told the club's official website.
"In the two games we've got coming up we've got to make sure we perform like we did when we hit our good spell when we won four games on the trot."
Allardyce also highlighted Andy Carroll as a potential factor in helping West Ham get back to winning ways, with the striker having only found the net once in the league this season due to injury problems.
"In the games coming up [Carroll will] be very important for us," he added. "The longer he carries on playing the better he's going to get. He'll get better as he gets sharper and we hope he stays fit.
"He laid two on for Kevin [Nolan] against Swansea [in a 2-0 win], he scored a goal against Stoke but didn't get the chance to score [against Manchester United]. If we provide the service he'll get the goals."