The Red Devils could have capped a brilliant season if they had won in Rome on Wednesday night but failed to apply themselves as the Spaniards took the prize.
But the Welshman knows the club will be aiming to redeem themselves.
“That’s what we’ll be aiming for,” Giggs told MUTV.
“Big teams have disappointments but they bounce back. That’s what we’ll be trying to do.
“It’s been a fantastic season when you consider what we’ve achieved this year – including our third league title on the trot.
“We just fell at the final hurdle. No team has defended the Champions League, it’s a very difficult trophy to win. We deserved to get to the final but we didn’t deserve to win.
“Barcelona did deserve to win. They are a good team and if they go one-nil up, they’re the best in the business at keeping the ball. They can make teams look ordinary.
“We didn’t really recover after conceding the first goal. In the second half we improved a bit but it just wasn’t to be.”