The Wales midfielder was devastated when the Hoops were dumped out by St Mirren in Sunday's semi-final clash at Hampden Park.
The shock 3-2 defeat cost them a meeting with Hearts in the final and ended any hopes of a domestic treble this season.
But Ledley said: "We've got the SPL, the Champions League and the other cup as well. We just need to concentrate on those, take it game by game and rebuild and go again.
"We've had a fantastic achievement already to get into the last 16 of the Champions League and hopefully we can get a fantastic result against Juventus and go from there. We know it's going to be difficult but hopefully we can achieve it.
"We are devastated as a team. It wasn't a good performance at all from us. It was a sore one for us and we just didn't get going.
"I'm not too sure why that was the case. We will probably watch the video again and see what happened. We were unlucky again but we need to punish teams from the off."
Charlie Mulgrew missed a penalty against the Buddies while Gary Hooper and Georgios Samaras both saw efforts hit the woodwork.
The Welshman added: "If you look at it now, it just wasn't our day. On another day, maybe it would have happened. But we can't make excuses. We just weren't good enough."
Bhoys boss Neil Lennon was furious with the result and accused his players of "behaving like spoiled kids" in his post-match briefing.
Ledley said: "He was devastated just like us. He told us he wasn't happy with the performance and the individuals."