The Scottish champions were shocked by the Kazakhstan club 2-0 at the Astana Arena on Tuesday night in the first leg of their Champions League playoff qualifier.
But Welsh midfielder Ledley believes the Hoops were desperately unlucky not to score and is expecting Neil Lennon's side to come out firing in Glasgow next Wednesday.
"We should have scored six goals easy, that's why," Ledley said.
"To be fair to them, their keeper was on fire but we dominated possession and had more chances but lost sloppy goals.
"It is definitely frustrating, we dominated them away from home and two sloppy goals killed the game.
"Away from home you need to keep the door shut and it just wasn't good enough today.
"But we believe we can score against them."
He added: "There is always pressure in the Champions League, it is a massive tournament and fantastic to be in. Hopefully the fans will behind us and we will need to put on a good show."