The Israel midfielder, who joined the Scottish champions from FC Ashdod in August 2013, signed a new five-year contract with the Parkhead club on Monday which ties him to the Hoops until 2020.
However, Bitton was on the periphery of Deila’s squad for the first few months of the Norwegian manager’s tenure before establishing himself in the side following an injury to Charlie Mulgrew and the 24-year-old has since become a key player for the Ladbrokes Premiership leaders.
Speaking at Celtic’s Lennoxtown training complex ahead of the crucial Europa League clash with Molde at Parkhead on Thursday evening, he was asked if there was a time when he thought he might have to leave Celtic.
“I will be honest, yes, because every player wants to play,” said Bitton. “It’s not because I wanted to leave Celtic.
“In the beginning I didn’t play much, even in the first year with Lenny (Neil Lennon).
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“I came here when I was 21 years old, it was first time away from home and Israeli football and it was a little bit difficult.
“The tempo in Scottish football is much higher than the Israeli league. I knew it before I came here but I didn’t realise the difference.
“I had a good conversation with him (Deila) last year. I didn’t realise why I wasn’t playing and when you don’t know why you don’t play, you cannot change the thing you need to improve.
“After the conversation with the gaffer I tried to change, tried to show him that I deserved to play and I got my chance.
“I tried to change a lot of things but the most important thing that the gaffer wanted me to change was the pace of the game.
“Sometimes in your career you have tough moments.
“But I am happy that I went through it, happy that I stayed here, happy that I signed a new contract and I think I am the happiest man in the UK now.”
Deila has been so impressed with Bitton’s progression that he recently said that the midfielder reminded him of Barcelona star Sergio Busquets - which flattered the Hoops player.
“Sergio Busquets is one of the best midfielders in the world so to be compared to him is something I dream about,” he said.
“But I have a long way to being Sergio Busquets.
“Sergio Busquets and these types of players, like (Nemanja) Matic, they play for the best teams in the world.
“You always need to learn from these kind of players, what they do in the game, what they do before they get the ball, and those type of things.
“But the most important thing is to improve myself every day, to do the things that coaching staff want me to do and to have success at Celtic.”
Celtic are bottom of Group A with two points from three games and go into the Molde match knowing a win is vital to their qualifying hopes following their 3-1 away defeat to the Norwegian outfit last month.
While accepting the need to take the game to the visitors, Bitton believes the home side will have to be wary.
He said: “We try to go 100 per cent from the beginning in every game at Celtic Park.
“But they are a very strong team, a very counter-attacking team and they hurt us in the last game.
“We controlled the game but conceded on the counter and then we needed to chase them so we will need to be careful.”