Saturday's goalless draw with Aston Villa extended West Ham's unbeaten run to five matches, with Sam Allardyce's side now sitting fourth.
Allardyce has overseen a remarkable transformation of his side this season and Diafra Sakho has been particularly impressive with seven goals in nine appearances.
Noble is encouraged by the form West Ham have shown in the opening 11 games and believes they can keep pace with the leading sides.
"It's a very good squad with a lot of competition for places," he told the club's official website. "We've got to thrive off that competition and want to get better.
"It's been a successful period for us since the last international break.
"We came back from Stoke after a big performance and got another point on Saturday, but most importantly a clean sheet and a good performance.
"We have to carry on and look forward to the next game. We can't dwell on how well we're playing or how many points we've got. We need to try to stay in this position as long as we can."
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