Ambrose - speaking ahead of next Tuesday night's second-leg game at the home of Scottish rugby- has been impressed with Deila, even if their relationship is only days old.
He said: "I have only been back here for a couple of days but the atmosphere is nice.
"I think everyone is settling in well but we need time to adjust to how he wants us to play.
"It will be a gradual process. We will co-operate, to give him all we can, so we can move faster because the Champions League is ready and the league is starting soon."
Ambrose also says he draws no distinction between playing against France in the World Cup or Icelandic minnows KR Reykjavik in a Champions League qualifier after again merging one season almost seamlessly into another.
The Nigeria defender's Brazil experience ended on June 30 with a 2-0 last-16 defeat by France in the Estadio Nacional in Brasilia, a match watched by 67,882.
After only a fortnight's break and only a couple of training sessions under new Celtic boss Ronny Deila, the 25-year-old was pitched into the first-leg of the Hoops' Champions League second qualifier against KR Reykjavik in Iceland on Tuesday night, a low-key affair played in front of around 1,500 fans.
Debutant Callum McGregor's late strike in the 1-0 win looks to have made next week's return game at Murrayfield stadium in Edinburgh a mere formality.
However, Ambrose, speaking at the club's Lennoxtown training complex, stressed the importance of focusing on the task in hand as he compared the difference in standards over his last two games.
"It was difficult but as the same time you have to respect everyone you play against in football these days," he said.
"You have to give your opponent due respect because (there are) no minor teams or minor countries in football these days, you can get beaten when you are not prepared.
"It would have been a story if we had got beaten.
"So it doesn't matter who we play against, the most important thing is to go out and represent Celtic and play as a Celtic player and to win every game we play.
"So that is the mentality."
Ambrose is noted for his indefatigability and has no concerns about having had only a few weeks off before starting what is sure to be another exhausting campaign.
The former FC Ashdod player, who moved to Parkhead in 2012, said: "It is normal because it is not the first time. I am a professional and I am used to it. It has been part of me. I am always ready to go. I just love playing football.