The Potters took a first-half lead when Jonathan Walters completed a cunning set-piece routine, firing past Jussi Jääskeläinen from close range.
West Ham, who remain in seventh place, restored parity in the 48th minute after Joey O’Brien converted Gary O’Neill’s low cross into the Potters net.
“Well we were unlucky in the end,” Nolan told Sky Sports. “We created enough chances to win it – I was guilty of missing two great chances.
“But to be fair, it’s a great result after going 1-0 down to Stoke, who made life tough for us and played well.
“It was a good game and a great point.”
Stoke midfielder Charlie Adam was also delighted to see the Potters gain a rare point on the road, while also revealing the work which went into Walters’ goal.
“It was a good point,” said Adam. “In the first half we were excellent but we switched off two minutes into the second half.
“When you’ve got quality players like Kevin Nolan and Andy Carroll, it’s difficult.
“So overall, we should be pleased with a point because West Ham are going well and it’s an away point.”
He added: “At this level, you need something different. This is a top league with top players and you need something extra to try and get an edge on another team.
“We’ve been working all week on it [the set-piece] and we knew there was a gap and if we could get somebody blocking one of their men and get Walters on the end of it.
“Fortunately it worked and we got ourselves deservedly in front.”