Neil Lennon's men have it all to do after the first-leg of the play-off against the Kazakhstan champions at the Astana Arena.
The home side found themselves ahead against the run of play in the 12th minute when Andrei Finonchenko scored from close range.
Celtic might have scored twice before then and the Hoops proceeded to create and miss more opportunities before and after Shakhter's powerful striker Sergei Khizhnichenko headed in a second in the 77th minute to leave the Hoops chasing the tie in the second-leg in Glasgow next Wednesday night.
Asked why he was confident of turning the tie around, the Wales midfielder said: "We should have scored six goals easy, that's why.
"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."
Ledley played down the pressure Celtic will be under to rescue the tie.
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."