Allardyce travels to Wearside to face a team that is three places further down the league than the Hammers and also four points worse off.
But Allardyce believes the Black Cats have performed better than their results have shown.
He said: "It's not been about the performance but the results haven't come because they have not converted enough of the chances that they've created.
"I don't think they've had too many goalscorers apart from the magnificent start (Steven) Fletcher made.
"I think they have paid a price for that in result terms but performances, particularly at Sunderland, have always been very, very good - according to our reports.
"It will be a tough game as always away from home. We want to be playing as well as we did against Manchester United to achieve a result at Sunderland. Anything less than that will make life difficult for us."
In last week's FA Cup clash against the Reds at Upton Park, it needed a last-gasp equaliser from Robin van Persie to salvage a replay for United.