The Hammers drew 0-0 at Liverpool this afternoon to move on to 37 points.
"I'd like another three points," he said. "Some of the teams below us are picking up two or three wins back-to-back, but we are looking up, not down."
The West Ham boss also had praise for his defence, who nullified Liverpool's attack.
Allardyce added: "I don't think we've defended better away from home all season."
West Ham's next game is away at Southampton on Saturday.