Giggs told MUTV: "When you concede a late goal it's always hard to take, especially having got ourselves back in the game.
"The luck just didn't go for us. Sometimes you get the breaks and Chelsea had them today. They cleared two shots off the line, they were given a penalty and Ronaldo got a dubious offside call when through on goal."
Giggs accepted Chelsea were dominant early on but was pleased with the fight United showed after the break, which culminated in Wayne Rooney's equaliser.
"Chelsea were the better team in the first half and we were disappointed because we didn't keep the ball enough," the Welshman said.
"But in the second half we played to our tempo and showed great character to get back in the game, so to lose the game to a penalty is disappointing."
Giggs knows the Reds must put the defeat behind them and focus on the remaining games, starting with Tuesday's titanic Champions League semi-final second leg against Barcelona.
"We've got to pick ourselves up," the winger added. "There's no bigger game than Barcelona. We want to win the league and we want to reach the Champions League final, and it's still in our hands.
"We showed our battling qualities in the second half today, and we'll need them in the next two games."