The Glasgow giants were reinstated into the competition by Uefa last week after Europe's governing body expelled Swiss club FC Sion who were deemed to have played five ineligible players when they met the Hoops in the second play-off leg.
Now that the men in green and white have been given another chance, Ledley says the players and coaching staff are not about to take it for granted whilst saying he is not bothered to replace Sion.
"I have no sympathy for Sion whatsoever and it's great to be back in European competition," Ledley told the Daily Record.
"It's important the Celtic fans see us in Europe playing against the best clubs and against the best players so it's all good as far as I'm concerned.
"We have not been in Europe at this stage for a couple of years now and a club of this size needs to be playing at this level.
"Also, the lads want to prove people wrong that we can do well in Europe.
"I know the fans will be planning a few trips now in Europe and that's fantastic.
"Hopefully they will enjoy the experience and we now need to improve from the Sion games. It's up to us to show the world how big this club is and prove to people we deserve this second bite at the apple."