The Hammers currently sit in 10th but still have to play the all of the top sides from now until the end of the season.
Allardyce led the East Londoners to a top half finish last season and is hoping to do so again, although that looked a long shot when they were stranded in the relegation zone back in January.
Tenth is the best West Ham can hope for this season, with the gap to 9th place evident, but Allardyce has put pressure on his team to make sure they are the team to grab the top half spot.
“We finished with 46 points last season and the challenge is to get close to that again,” Allardyce wrote.
“Realistically, with Southampton one place but 11 points better off, 10th is as high as we are going to go.
“We may be halfway up the table but we need a few more points yet.”