Sam Allardyce's side lie 15th in the Premier League table, just two points clear of the relegation zone ahead of this weekend's fixtures.
The Londoners have conceded just eight league goals all season, with Southampton and Tottenham the only teams with meaner defences.
But they have managed to score only eight goals themselves, a factor which Nolan concedes has prevented them from climbing the table.
"When you look at the performances we've put out this year I think we should be a lot higher," Nolan told Weekend Warm-Up.
"We've ended up being in and around the bottom three for most of the season but to have six clean sheets at this stage of the season, 10 games gone in the Premier League, you can't really ask for more.
"It's just down to us now to start putting the ball in the back of the net, that's the be all and end all."
Nolan scored 10 goals for West Ham last season, including a hat-trick in their 4-2 victory over Reading on the final day of the campaign.
He has struggled for goals this season though, with his only one to date coming in the opening day win over Cardiff, and with his side usually going on to win matches he scores in, Nolan is keen to find his goalscoring touch once more.
"When I score, we win games!" he added. "There's no doubt about that, when I score a goal I want to make sure it means something and we go on to win a game.
"I'm not about personal accolades or trying to score just to get my numbers up.
"I've got to score goals, that's a major part of my armoury if you like. I'm feeling that I'm starting to get the chances again."
Nolan will go up against an old team-mate from his Bolton days on Saturday, with Sweden striker Johan Elmander now leading the line for Norwich.
Elmander has fond memories of his time at the Reebok Stadium and feels Nolan remains a major threat in front of goal.
"He's been up on the top for so many years and he's always delivering, he just keeps on going," he said.
"He's always fighting and giving everything in every game. He'll turn up in that hole where the ball is coming, and when he gets the chance he puts in the goal. That's something you're born with."
Elmander admits he is looking forward to testing himself against a number of former Bolton team-mates, but insists he will do them no favours on the field.
"I think there are four or five of them there now, Jussi Jaaskelainen, Kevin Nolan, (Ricardo) Vaz Te, (Matthew) Taylor and Andy O'Brien," he added.
"It's good friends of mine, they were really nice to me when I was up in Bolton so it's going to be something special to play against West Ham.
"But when you're on the pitch you don't think about that much."
Watch Norwich v West Ham live on Sky Sports 1HD from 5pm on Saturday.