Chelsea keeper Petr Cech appeared to carry the ball over the line on an effort from Giggs.
Giggs said: “It was clearly over the line – that’s what I was asking for. I could see it was over the line and the referee didn’t give a free-kick so it was a goal.
“I felt I was getting to the ball quite comfortably and felt someone touch my leg.
“But I was claiming for the goal not the penalty.
“We’re disappointed obviously. The big decisions didn’t go for us and if you don’t get the big decisions it is going to be hard for you.
“The referees are picked on merit and how they perform throughout the season.
“The FA Cup is a big occasion and you want the referees to get the big decisions right. They are only human and sometimes they get them wrong but in the Cup final you hope they get them right and today they didn’t.”