Nolan thought he had given his side the lead after just five minutes but play was called back for offside, although replays suggest that this was an incorrect call.
The match finished 0-0 and Nolan believes that such luck favours the league's top teams.
"It was important after last week's defeat [at Wigan] to put in a performance. We know we're going to be a match here for anyone and we were today," said the midfielder.
"We were unlucky with the offside - it was a goal. Champions get luck like that. The referee got it wrong."
The result leaves the Hammers eighth in the Premier League table, while City remain third.