The Frenchman started his Parkhead reign with a 2-1 home loss to Hearts on Sunday that left the Scottish champions three points adrift of the Premiership leaders with a game in hand.
Nancy attracted much comment for using a hand-held tactics board at pitch-side to inform players of changes, while one radio broadcaster even questioned his choice of green trainers.
But the 48-year-old former Columbus Crew and Montreal boss, speaking ahead of Celtic's Europa League game at home to Roma on Thursday, said: "People deserve the right to talk.
"I'm going to dress one way, maybe they are going to say that they don't like the way I dress, so I don't waste time on that.
"If I use it (the tactics board), it's because it's good for me. Simple as that and I'm not saying that I'm going to use it all the time."
He added that since moving into coaching he has taken the decision to block out outside noise on social media.
"This is part of the job. That's why we study for that. And after that, I'm not here to comment on everything," he said.
"Me, I control what I can control, to be good with my players, with my club, with the people that I work with."
Nancy revealed his mother was concerned about the effects of the whirlwind start to his time with the Glasgow giants, which features a Scottish League Cup final against St Mirren at Hampden Park on Sunday.
"My mum told me that I have bags (under my eyes)," he explained. "I said, 'Yeah, mummy, I just came in, jet-lagged, trying to anticipate everything'.
"But again, this is part of our job. I'm really excited by that. So, I try to stay at peace with myself, at peace with you."