After falling two goals behind in the opening 22 minutes at Old Trafford on Saturday the visitors fought back to halve the deficit before half-time.
The dismissal of Wayne Rooney gave West Ham a man advantage for the final half 30 minutes and they thought they had rescued a point when Nolan fired home in the closing minutes.
However, the midfielder's effort was ruled out for offside.
Despite that disappointment Nolan believes West Ham's attacking play promises big things for the club, with a top-half finish a priority.
"We have to get into the top 10 – that is a realistic aim," said the 32-year-old. "We still have a lot of injuries and I've just come back, as has Carl Jenkinson.
"But because of the acquisitions, if we can keep that performance high and the tempo high, it's exciting times for us.
"We really deserved a draw and when it comes to a decision by the official that takes it away from you, it's disappointing.
“I'm gutted but there are lots of positives to take away. I'm just hoping we continue to play the way we have done over the last few weeks.
"If we do that we will get the results we deserve. We just have to eradicate the sloppy mistakes this year if we want to be successful.
"We've got goals in everyone now across our front line. We still have a lot to learn, but I'm really looking forward to the rest of the season."
Sam Allardyce's side, who finished 13th last season, are currently 12th.
