Allardyce: West Ham 'not out of the woods yet'
An unbeaten run of four Premier League matches - including three consecutive wins - has seen the Upton Park outfit climb to 11th in the table, giving them some breathing space in the battle against relegation.
But Allardyce does not feel his charges can afford to take their foot off the gas ahead of their home meeting with Southampton on Saturday.
"Our problem early in the season was scoring goals to win the points," he said. "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.
"We have to maintain our good form when we play Southampton (on Saturday). There's a long way to go to get safe so we have to keep it up.
"The basics will always stay the same but we might have changed the training a bit around this good run. Try to take the pressure off and keep them focused on getting it right in both boxes.
"We've made great strides and great efforts, everybody's played their part to try and alleviate the situation we were in, but we're not out of the woods yet."
Allardyce was reluctant to talk about Ravel Morrison, who has been loaned out to QPR, insisting: "My focus is on the squad of players I've got here."
However, the former Newcastle United boss does not feel the attacking midfielder had played his last game for West Ham.