The Hammers lost to Spurs 1-0 at home on the opening day of the campaign and fell to a 2-1 defeat to Everton at Goodison Park last month.
Nolan, who has been on the books of West Ham since 2011, claims that Sam Allardyce’s side deserved to pick up points from those encounters.
“I'm delighted to be in a team that's won," West Ham’s official website quotes the 32-year-old as saying.
"In my third start I got there in the end! Saying that, I thought we deserved something at Everton and we definitely deserved to beat Tottenham on the first day of the season.
"It's nice [to win] and I'm delighted to get another goal. It's my first of the season and hopefully the first of many. I felt good before the game, I've been training hard and just waiting for my chance.”
Nolan was speaking following West Ham’s 2-1 victory over West Bromwich Albion away from home in the Premier League on Tuesday.
It was the former Newcastle United star’s only third start of the league season, and he found the target in the 35th minute.
The win has lifted West Ham up to fifth in the Premier League table with 24 points from 14 matches, just a point behind fifth-placed Manchester United.
Next up for West Ham is a Premier League clash against Swansea at the Boleyn Ground, and Nolan is looking forward to scoring once again.
"I've got a goal and I'm looking forward to another game against Swansea,” said the ex-Bolton Wanderers star.
“I’ve got quite a good record against them from last season and I'm feeling good so hopefully I'll get my chance and score another couple.”
West Ham are having a truly great season, and although no one expects them to finish in the top four, a place in the 2015-16 Europa League is well within reach.
The month of December will be crucial for the Hammers in their quest to achieve that objective, and judging by their win against West Brom, it seems that the players are fully aware of it.