A nervy 2-1 win over Spartak Moscow at Parkhead enabled Neil Lennon's Hoops to finish runners-up in Group G with 10 points – their best-ever return in the tournament.
The club will now progress to the knockout stage for the third time in their history, and could come against Sir Alex Ferguson's Manchester United, Juventus, Bayern Munich, Borussia Dortmund, Malaga, Schalke 04 or Paris St Germain in the December 20 draw.
And Ledley believes the manner in which a team who were the fourth seeds in the group, performed against Barcelona, Benfica and the Russians, ought to make people sit up and take notice.
And it is not just those who will come calling from the Continent who should be looking to what Celtic have achieved this season, according to Ledley.
"It is not just in Europe people should be thinking we are owed a bit of respect; it is those south of the border too," said the Welshman. "I obviously had a lot of people question my choice when I came up to sign for Celtic and there were people who claimed I had no ambition because I didn't go to the Premier League.
"Now I have a chance to play in the last 16 of the Champions League which is a phenomenal achievement.
"The performances we have put in and the results we have had should certainly mean people shouldn't look to us to be an easy touch when the draw is made. We have shown that we deserve to be treated with some respect.
"We are a young team and before last season there weren't many of us who had much European experience at all. Now we feel we are capable of going out and mixing it with anyone."
Ledley has insisted Celtic will have no fear when it comes to the next round of the tournament, the first leg of which will be played at the end of February.
Given that they have gone through the the competition as underdogs, Ledley believes Celtic can continue to buck expectations.
"We have played against Barcelona, the best team in the world, and beaten them here," he said. "We have to go forward with confidence now. It was a nervous game against Spartak but, overall, we deserved to get through.
"It is a cracking chance for us and why can't we go any further? Who is to say what might happen? I don't think we should go into the last 16 thinking we have gone as far as we can.
"Everyone was quick to write us off when the draw was made for the group stage, so we will go forward with confidence and belief in our own ability."
And Ledley believes skipper Scott Brown was hugely influential in getting Celtic through to the latter stages.
"Scott has played a real captain's part," he said. "We all know he has gone through a lot of pain this season with the injury he has and now we'll see whether he is rested or goes under the knife.
"But he has made an enormous contribution to the Champions League campaign and I think we can all appreciate that."