West Ham currently sit in ninth and Noble doesn't want them to finish any lower.
In an interview with the London Evening Standard, Noble has reflected on the side's recent form that has seen them slide down to ninth place in the division after a promising start to the season.
The Hammers have won just the one game in their last 10 and the likelihood of them achieving the European qualification that manager Sam Allardyce has been talking about for much of the season seems to slipping away.
Noble said: “I think everyone knew, the way we started the season, we couldn’t maintain that sort of pace. Very rarely does a club creep into that top six that doesn’t really belong there.
“The League is sorting itself out now and the teams you expect to be up there — are there.
“We don’t want to drop down any lower than we are at the moment, though. We want to push on. All teams have a bad run but I don’t think that applies to us because in recent matches, we’ve drawn at home to Manchester United and away at Spurs — and both games we should have won."
Going into tonight's game against Chelsea at the Boleyn Ground the Hammers sit in ninth place - one point behind Swansea City but they have Stoke City breathing down their necks. The meeting with Jose Mourinho's men would be another tough fixture out of the way in the second half of the season before they enter the last ten games of the campaign.
A top half finish will have represented some progress on last season, as they spent much of the first half of the last campaign in a precarious position towards the foot of the table. However, there will be a tinge of disappointment at the way things have gone since the Christmas period, especially with their inability to close games out against the likes of Manchester United and Tottenham Hotspur, where they conceded equalising goals in the dying minutes.
But there will have been a lot of people at the start of the season who would've said that a finish in the top half of the Premier League will have represented a pretty good season - but there is still that desire to perform better.