Rooney fired his effort over the crossbar in United's 1-0 win over West Ham in Wednesday night's FA Cup third round replay at Old Trafford.
The England striker has now missed two penalties this season and 10 in total for the club, with the team as a whole faring little better, having put away just four spot-kicks from nine.
But Giggs recalls Ruud van Nistelrooy going through a similar poor run for United before rediscovering his penalty form and Giggs has backed Rooney to do the same.
"Players sometimes go through these types of spells," said Giggs. "Ruud van Nistelrooy missed three on the trot. Not many people remember that but I certainly do.
"The fourth one he stepped up, buried it and probably didn't miss one again.
"Wayne is our penalty taker. He will be disappointed because he is a goalscorer who wants to score goals but I am sure if we get another, he will take it."
Giggs would not be drawn on how long he will extend his time at Old Trafford for but he turned in a man-of-the-match performance against West Ham, prompting Sir Alex Ferguson to insist he could remain on the playing staff for at least one more season.
"I am not thinking about my contract at the moment. It is like previous seasons, I am quite relaxed about it," added Giggs.
"I am just enjoying my football. There are so many crucial games at the moment I am not too bothered about what is happening next year.
"I feel good though. Obviously the manager knows how to look after me and I try and look after myself as best I can, which you have to at this age.
"I am not going to play every game but I have to be ready and prepared when called upon."