The Hammers all but secured their survival on Monday night as a 2-1 win at Sunderland saw them clinch a sixth victory in nine games.
Noble now hopes that he and his teammates can move further up the table and seal a top-half finish before the end of the season.
"The win on Monday put us on 37 points and that's great for the club. I thought we played well at Sunderland - we defended really well and they had to make the substitutions to change the game," he told West Ham's official website.
"I think you have to look back at the position we were in around Christmas time. We were second from bottom at one point and now we've shown to everyone what we can do.
"We've got six games to go, we want to give a good account of ourselves and our aim is to come 10th."
West Ham continue their Premier League campaign on Sunday when they entertain leaders Liverpool.