West Ham grabbed their first win in four games when they came from behind to beat managerless Tottenham 2-1 with Modibo Maiga heading the winner late on.
Allardyce's side travel to Manchester United on Saturday having not won at Old Trafford since Carlos Tevez's goal helped them avoid relegation to the Championship in the 2006/2007 season.
"For me, the challenge is to get the players to kick on from this," Allardyce told the club's website after beating Spurs away for the second time this season.
"When we beat them last time, I thought we'd go on a run of results and pick up more points than we have done.
"I don't know where we'll go from here but it's just a fantastic result and the lads are absolutely delighted."
West Ham are 17th in the Premier League and one point above the relegation zone, but they can take inspiration from Everton and Newcastle United who both recently won at Old Trafford for the first time in 21 and 41 years respectively.
After facing champions United, West Ham play league leaders Arsenal at home on Dec. 26, before managerless West Bromwich Albion visit Upton Park two days later.