The Irons looked to be heading into the fourth round after two headers from James Collins - powering in crosses from returning fans' favourite Joe Cole - had turned the match around following Tom Cleverley's opener in the 23rd minute.
However, with 90 minutes already played, substitute Ryan Giggs sent a long, crossfield ball up towards Van Persie, and the Dutchman, who had started on the bench, took it in his stride before stroking a sublime low shot into the far corner.
Nolan accepts one of United's great strengths is always playing until the final whistle goes - whenever that may be.
"I was baffled by the four minutes, but you have to get on with it and see if you can see it through. Unfortunately we could not do it," said Nolan.
"Everyone realised it should not have been four minutes.
"But you will have to ask (referee) Mr Atkinson that, because I am not getting a fine.
"But it tends to happen, and it is no thing towards big teams.
"Manchester United have done it for years, they have been fantastic and a top team, hats off to them because they go to the final whistle.
"It is not like we have gifted them a goal, they have brought a pure quality move."
Nolan continued: "When you see it in real time, what a touch and a finish, what a ball.
"That is why they are champions and win trophies year in and year out, because they have got special players who can do special things in an instant.
"However, you feel so gutted because I thought if we had won, we would have thoroughly deserved it."
Despite the clear disappointment of not being able to see the result through, Irons boss Sam Allardyce also admits it is difficult not to be in awe of United and the class of Van Persie, who now looks something of a bargain even at the £24million paid to Arsenal.
"Twenty goals in whatever, 28 games, answers that. The man himself picked the team where he thinks he can get the most trophies, not make the most money, and that is to his credit," said Allardyce.
"He is at that team he wants to be successful, and as a professional he wants to hit the ground running. He has already shown everyone what he can do."
He added: "It is hard for me to criticise the players and say if you had done this or that you could have stopped it and say it is our fault we have drawn.
"Before we knew it, in a split second, from the ball being on the halfway line and in a non-dangerous position, with us having seven or eight behind the ball... the goal was so silky and smooth."
Cole, 31, impressed on his return to the club he had played for as a teenager, leaving for Chelsea in 2003.
The one-time England regular hopes the Hammers will soon see the best of him again.
"All the eyes were on me, but I am just happy to be out there playing and getting match minutes in and getting stronger," said Cole.
"It is important we keep performing with that kind of desire and keep the club in the Premier League this year, then build from there and go on."