The Hammers slipped to a 3-1 defeat to Arsenal on Boxing Day despite taking the lead, and Allardyce has urged his men to move on quickly ahead of clashes with fellow strugglers West Brom and Fulham.
"Our big games are the West Broms and Fulhams in the next two games," Allardyce said. "It is about performing like that against those clubs, which give you a better chance to win the game.
"We have to believe, at the end of the day, that we will convert the chances as we did, certainly the home game a few weeks ago against Fulham.
"West Brom is becoming a must-win, so we have to go all out without being over anxious or over adventurous because if we start leaving back doors open and start conceding too many goals.
"The chance to catch up is getting a little wider and wider each game when you don't pick up points.
"But we have to take a lot of positives out of the way we played against Arsenal and make sure we played like that, like we did at Tottenham in the cup against West Brom.
"When we've had that opportunity recently, we haven't done that. We haven't played as well as that, apart from when we beat Fulham 3-0 here.
"We played Sunderland here and never got to this level so ended with a draw. We played against Aston Villa at a high level but didn't score. We played at Crystal Palace and lost and lost after going 1-0 up against Norwich.
"They are key let-downs. You can always lose to Arsenal even if you play your best. It is disappointing for the lads when they have put such a big effort in and made so many chances against this team and not finished the game off."