scored a stoppage-time equaliser to secure a 2-2 draw.
Giggs, who had just headed a seemingly easy chance over from close range, sent a 60-yard pass over the home defence and van Persie then beat West Ham goalkeeper Jussi Jaaskelainen from a position on the right of the penalty area.
"We missed some good chances, with headers over the bar and Shinji Kagawa had one blocked on the line, I thought it was not going to be our day," Ferguson admitted.
"But you have to say the pass from Ryan Giggs, then the first touch from Robin and his finish were world class."
The replay will add to an already-congested fixture list for United, who will resume Champions League action next month, but Ferguson made it clear the FA Cup was still a competition he wanted to win.
"We want to stay in it and have a go at it this year," he said. "We have had some terrible draws over the years and been knocked out early and we don't enjoy that."
Tom Cleverley gave United the lead midway through the first half but within four minutes James Collins had headed in an equaliser from a delivery from Joe Cole, who was making his first appearance in almost 10 years for West Ham, his first club, following his transfer from Liverpool.
Collins then headed in another accurate cross from Cole after the break and Sam Allardyce's side made it to the final minute with their lead still intact.
Ferguson was not pleased to have conceded two almost identical goals.
"For us to be losing 2-1 in that game is amazing with the way we played," he added.
"But when you play West Ham you have got to defend those crosses and set pieces, because they are brilliant at that -- the best team in the league -- but we did not do that.
"Twice in the same position, it was James Collins from a cross by Joe Cole and we have lost two goals. I could say it is a travesty, but they are good at it, but with some of the chances we missed, we should have been home safely."
Allardyce, who regards Ferguson as a friend and mentor, was disappointed not to be celebrating a famous victory.
"It's more than a tad disappointing," he said. "But you have never beaten Manchester United until the final whistle blows and I have learned that in the past.
"It was just a brilliant goal they scored. The first one was good enough, for me, but the second goal, the ball from Giggs, who smashed a half-volley over James Tomkins' head from about 60 yards and van Persie's first touch and finish were just unbelievable.
"Sadly for us it was an equaliser with just a couple of minutes to go. We had one cleared off the line, we were very patient and tactically we were very good. We have conceded two goals and I can't really remember what Jussi had to do.
"We almost feel like we have lost in that dressing room when you get done like that in the last minute. But we are still in the hat."
Cole was applauded of the pitch when he was substituted late on and Allardyce added: "It's obviously a fantastic debut for him and a great reception from the fans, which must have made him feel really good, but the whole team has played really well."
Meanwhile, West Ham are close to signing forward Wellington Paulista on loan from Cruzeiro, according to the Brazilian club.