Allardyce's men are six points clear of the relegation zone in 10th ahead of Saturday's visit to Stoke City, following a run of four wins in their last six games.
The London club slipped to a 1-0 defeat in their previous league encounter at Everton at the beginning of the month, but Allardyce is keen to finish the season in fine form and ensure West Ham's top-flight status.
"It's 10 games to go, 10 very important games to try and achieve as many points as we possibly can," Allardyce said.
"We'd have to say at this stage of the season it's about how quickly can you get safe. How quickly as a squad of players can you achieve the results you need to achieve to secure your position in the Premier League.
"Then it's an opportunity to ease the pressure on the players that everybody has at this stage of the season.
"You see how far then you can finish in the league. First priority is how quickly can you achieve safety, and then from there it's about whether you can go on from there."
Joey O'Brien and Marco Borriello are the only players absent for West Ham this weekend and Allardyce is keen to capitalise on the club's relatively clean bill of health.
"Our squad is pretty good at the moment," he added.
"There's only a long-standing injury to Joey O'Brien - a shoulder dislocation - and the only other unfortunate one is Marco Borriello, who hasn't recovered from a calf strain.
"We've had it pretty good recently (in terms of injuries), and I've always said that's why results have turned in our favour along with (a) determination and desire to go out and turn the season around.
"The players have done magnificently well up to now, and we'd like to continue that between now until the end of the season."
