Giggs, named as captain for the evening, delivered a virtuoso display in the contest at Old Trafford as United set up a fourth-round home clash with Fulham.
And referring to the 39-year-old after the game, Ferguson said: "He will play for another year.
"There are no signs of tiredness or weakness in his game, his quality is still there, he has fantastic balance and he has appetite for it.
"He is just an incredible human being."
United's goal came in the ninth minute from Wayne Rooney, who was back in action after sitting out their last five matches due to a knee injury.
The England striker turned in Javier Hernandez's square ball from close range, and after taking the congratulations of his team-mates, then paid his respects to his late sister-in-law, kissing his hands, looking to the skies and raising his arms as he walked back towards the halfway line.
United had chances to extend their advantage but could not take them and West Ham grew into the game after the break.
The visitors had a penalty appeal for handball against Rafael waved away by referee Phil Dowd, who then awarded a spot-kick at the other end with just over 10 minutes remaining for a similar infringement by Jordan Spence, only for Rooney to waste the opportunity by blazing high over the bar.
It leaves United with a record of four penalties scored and five missed for the season so far and Ferguson said: "I don't think it is just one of those things. I think we have to improve at that.
"If you get a penalty kick, really. . . there has been talk about (the good penalty record of) Rickie Lambert at Southampton. That is what taking penalty kicks is about.
"There have been several great examples over the years - (former Southampton midfielder) Matthew Le Tissier scoring 47 out of 48.
"A penalty kick is your opportunity to take advantage of a foul or a handball or whatever and score a goal."
West Ham manager Sam Allardyce was very unhappy with Dowd's decision-making on the two handball incidents and suggested the referee lacked courage.
Allardyce said: "It was very disappointing that we were not given a penalty at 1-0 in the second half for Rafael's handball, which was blatant and clear for the referee to see in the position he was in.
"He couldn't find the courage to give it unfortunately, and he then went down the other end and there was a very similar incident with Jordan Spence and it was given.
"That is a very big disappointment for me - the lack of consistency in that area."