The Hammers moved up to sixth in the table when Nolan's first-half winner clinched a 1-0 victory at his former club Newcastle on Sunday.
Many tipped Sam Allardyce's men to struggle after they booked their top-flight return with a narrow Championship play-off final victory over Blackpool in May.
Allardyce strengthened his promotion-winning squad by signing a number of experienced Premier League campaigners, including Jussi Jaaskelainen, James Collins and Andy Carroll, in the summer.
And they have made a healthy start by taking 18 points from their opening 11 matches.
Nolan said: "If people have been surprised by us so far, then that's their fault for underestimating us.
"We added some more quality to the squad that we came up with in the summer, so we knew we had a chance of finishing in the top 10. We're looking like we can do that."
Meanwhile, Nolan says he has no ill-feeling towards Newcastle chairman Mike Ashley and manager Alan Pardew following his exit from St James' Park.
The 30-year-old swapped Tyneside for East London in the summer of 2011 after Ashley refused to hand him a long-term contract.
Allardyce swooped in a £3m deal for his former Bolton skipper, who helped fire the Hammers back into the Premier League with 13 goals.
Nolan said: "I needed to get the best for myself and Newcastle needed to get what they felt was the best for them.
"I'd shake the owner's hand as willingly as I'd shake Alan Pardew's, because I got on well with them and they were good to me.
"I hope there is no animosity between us. I built up a great relationship with people while I was Newcastle."