The Hammers beat Wolves 3-2 to move into fourth spot in the Premier League table with eight games to go and Noble has promised that the club are going to have a "right go" in their bid to qualify for Europe's top competition next season.
The West Ham captain said: "We said two or three weeks ago that when we get to single figures in games left we can have a right go, because we have nothing to lose and we can go for it.
"Let's hope it's a great [season]. We have eight games to go and we're in fourth We're mixing it with the top teams."
Hammers boss David Moyes echoed the thoughts of Noble and has suggested that there is no reason why they can't qualify for the Champions League.
He said: "I am hearing pundits talking about West Ham having a chance of Champions League.
"Nobody would have envisaged or mentioned that last season. Can we keep it going? We are going to try and compete with the big teams right until the end."
On-loan midfielder Jesse Lingard continued his impressive form by scoring the opening goal and Moyes sought him out after the game for praise.
He said of speaking to Lingard at full-time: "I was telling him how well he has played.
"I'm probably a manager who doesn't say that very often, but he deserved that after his performance."