Defeat to Hearts at the weekend left the Hoops trailing SPL leaders Rangers by 10 points and languishing in third spot behind second-placed Motherwell.
But Ledley insists the belief in the dressing room is as strong as ever and he believes there is still plenty of time to make up ground in the title race.
He said: "The supporters have always been behind us from minute one so I would ask them to keep doing that and I think all of us in the team believe we can do it.
"We were disappointed with the results lately but we are all together in this to get back on track.
"It's still early doors at the beginning of the season so hopefully we can get together and get on a good run.
"There are loads of games left. We still have to play Rangers three times and Hearts three times, so there are still loads of points to go for.
"It's going to be difficult but there are still loads of games to play.
"We have good players here at this club and obviously we've been hit by the injuries but I think we've got to get over that now, push on and get as many points as we can."
Ledley is one of a number of injured players after being sidelined with a groin problem.
And, although disappointed not to feature for Wales over the coming days, he is relieved the international break means less chance of missing any more matches for Celtic.
He told the club's official website: "My injury is much better now and is coming on well. It's been a week today.
"I don't want to rush it so I won't be training until Monday hopefully.
"I would have missed another match and it's obviously good for me as I'll be back playing for Celtic.
"But I'm going to miss the next two Wales games which is disappointing. In the last few games we've done well and it would have been nice to have been part of it again."