Ledley told BBC Sport Wales' The Back Page: "I think if we had got promoted I would have stayed, but these things happen in football."
He now hopes Cardiff succeed where they failed in what he predicts will be the "easiest" of forthcoming seasons.
He said: "It's going to be one of the easiest seasons to play. I wish the boys all the best."
The Bluebirds' loss to Blackpool triggered the events that prompted Ledley to move after almost two years of speculation over his future.
Had he moved on before his contract expired or joined a Premier League club after it did so, cash-strapped Cardiff would have received substantial compensation.
Moving to the Scottish Premier League in a four-year deal denied the Bluebirds a much-needed financial boost, leaving some fans unhappy.
But the player defended his move to Celtic, believing it was his only realistic option of playing at a premier level in the circumstances.
Ledley said: "Stoke and West Brom were interested, but there was no formal bid. Stoke offered two players for me and Cardiff rejected it, so basically it was only Celtic and I wanted to go to Celtic in the end."
He admitted life was sometimes awkward at Cardiff during his last two seasons there.
"Some of the fans didn't know what was sort of going on inside the club and things like that," said Ledley.
"But I just wanted to concentrate on my football and try and get Cardiff promoted last season and obviously we failed in that, but hopefully they can do it again, hopefully they can get promoted this season.
"I think if we had got promoted I would have stayed, but these things happen in football and credit to Blackpool, they won the game and maybe if we won that game I would still be a Cardiff City player, but I think it was time for me to move on.
"Some of them [fans] have been positive. Quite a lot of people wish me all the best, saying I've been a great service to the club and "we've enjoyed watching you play" and obviously some of them haven't been the nicest.
"But they don't know what happens inside the club."
Ledley hopes the Bluebirds can hold on to the likes of star goal-getters Jay Bothroyd and Peter Whittingham, but fears they too could leave at the end of their contracts next summer.
Ledley said: "They've got four or five people out of contracts at the end of the season.
"The team's great and I think they've got a great chance this season - its going to be one of the easiest seasons to play. I wish the boys all the best."
But the 23-year-old has no regrets over his move to Celtic, saying pre-season friendlies against the likes of Manchester United are an indication of the club's status.
He said: "Playing the likes of Manchester United, Sporting Lisbon, Arsenal, Lyon in pre season games, you know it's a massive club - people want to play Celtic.
"Obviously, my ambition is to qualify for the Champions League and play Champions League football and hopefully win the league and win a couple of trophies as well.
"I haven't won anything in my career, I think it's time now in my career and I can go and win some trophies."
Source: BBC Sport
In a separate interview with Wales On Sunday Ledley has a pop at Peter Ridsdale.
"The supporters should have a go at Peter Ridsdale, not me, said the new Celtic player.
"He was the one that messed me about for more than two seasons; he's the one to blame for me leaving.
"If it was not for him I would probably still be a Bluebirds player today."
The relationship between the two men wasn't helped when Ridsdale told Cardiff supporters at a meeting last December: "Joe is playing as if he is playing somewhere else."
Ledley was not impressed.
"He hardly talked to me yet went on the record to say that I was not playing up to my usual standard and that it could have been because my mind was elsewhere. That was laughable," said Ledley.
"How many chairman criticise one of their players in public?
"Yet he knew I was injured and trying to help the club."
The full interview and story can be found here.
Source: BBC Sport