Unbeaten in the last four and with three wins on the bounce, the Hammers have flown up the table and now sit in 11th spot in the Premier League.
Despite having put some daylight between themselves and the other relegation-threatened sides, Allardyce is keen for his players to keep fighting and not to get complacent.
“Our problem early in the season was scoring goals to win the points. Now everyone is fit we’re putting both together.
“There’s more competition for places. Winston Reid can’t get in at the moment because the players who are starting are doing a fantastic job.”
He added: “We have to maintain our good form when we play Southampton. There’s a long way to go to get safe so we have to keep it up.”
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.
Chesterfield boss Jack Lester felt his side were unlucky not to claim all three points after their 1-1 draw at Cheltenham.
New Swindon manager Phil Brown revelled in his side's victory at Cambridge in his first game in charge.