Both teams progressed to the semi-finals of the Capital One Cup on Wednesday night, with West Ham coming from behind late on to score two goals in five minutes to beat Tottenham at White Hart Lane.
Allardyce's men lie 17th in the Barclays Premier League - one place above the relegation zone - and know they face a difficult task against David Moyes' side at Old Trafford this weekend.
The West Ham manager admitted that while he is not satisfied with the club's current league placing, he is delighted with the attitude, application and determination his players are showing.
"I'm not happy with the way things are progressing because we are in the position we are," Allardyce told skysports.com. "I expected us to be in a better position than we are but what I am happy with is the amount of work the players have put in, the amount of commitment they shown as a team to try and win.
"The end result is we have not won the games that we should have done. We certainly are creating the chances and we're certainly doing our very, very best to try and improve the situation."
Allardyce added: "What goes against us at this moment in time is too many key players injured and suspended.
"Once we overcome that I am confident we will improve our position in the league and improve our results."