The Bhoys midfielder was part of the team that beat Barca at Celtic Park earlier this month but qualification is now out of their hands with one game remaining after defeat at Benfica.
Neil Lennon's side need to better Benfica's result in Barcelona when they host Spartak Moscow in Glasgow next month and Ledley feels that is a must after all the work the players have put in.
"It would be unthinkable if we did not get through to the knockout stages now after all we have done in the competition," the 25-year-old told the Daily Record.
"As players we would be absolutely devastated if we ultimately fell short and didn't make it through.
"It has been a dream for me to play in the Champions League. It's what I came to Celtic to do and hopefully we are still in the tournament after we face Spartak Moscow.
"Of course, the result against Benfica was a disappointment, but the real positive is we still have a great chance of going through if we beat Spartak at home.
"If we give it 100 per cent in that final game in front of a packed crowd at Parkhead we have a great chance.
"I still believe we are favourites to progress. Hopefully, lightning won't strike twice and Barcelona won't lose again in this group.
"They are one of the finest teams in the world - not just of this era but of all time - and I hope they secure the win over Benfica and we can grab a result against Spartak Moscow that would see us go through.
"The manager has told us that we just need to pick ourselves up after Benfica. We need to get over it and hopefully put things right when Moscow come calling in a fortnight."
The Wales international realises that will not be a straightforward task against the Russian side but admits the players are desperate to finish off the job.
"We know it will be difficult against Spartak," added Ledley. "We had a fantastic result against them in Russia but they are a still a great team.
"They have nothing to play for now, they are out so the pressure is off them and I don't know how that will affect how they play against us.
"Our focus is only on Celtic and how we perform and if we give our all we can secure the win.
"We will be going all out to get the result we need to qualify for the last 16. We have come all this way and now we are all desperate to finish the job off.
"If we look back at the Benfica game then, in the cold light of day we will realise we didn't create as many chances as we had hoped.
"But we have to be fair on ourselves too because we knew the Stadium of Light was always going to be a difficult place to go and get a result.
"And we defended magnificently again as a team and as a unit. Everyone put their bodies on the line for the cause but what cost us at the end was switching off."
"Concentration is key at this level and unfortunately ours let us down towards the end and it proved costly.
"Even still, we had a couple of late chances and we might have grabbed an equaliser that would have taken us through to the knockout stage already.
"That only goes to show how fine the margins are at this level."