Neil Lennon's men were today part of the draw for the last 16 of the Champions League, with Juventus, Paris St Germain, Schalke, Malaga, Borussia Dortmund, Bayern Munich and Manchester United all possible opponents.
Mjallby was quick to downplay the notion teams will fear travelling to Parkhead, where Celtic beat Barcelona en route to qualifying for the knockout stages, but knows the players thrive in the arena.
Asked if opponents will be wary of travelling to Glasgow, he said: "Or will they want to come and experience the atmosphere?
"Most of these teams have so many experienced players, they've been all around the world.
"For us it's just brilliant. We know when we play at home we have this atmosphere and the supporters behind us and obviously it's going to make us better. At home we can beat anyone.
"We don't fear anyone because we've taken a lot of confidence from the performances in the Champions League so far.
"The players know now they can do something. The first target was to go through from the group stage and now we're in the last 16."
Mjallby hopes Celtic's squad remains intact over January, with the last 16 of the Champions League an incentive for players like striker Gary Hooper, midfielder Victor Wanyama and forward Georgios Samaras to stay on.
"This should be a great incentive for them to stay here at Celtic and take us forward," Mjallby said. "You never know where it's going to take us."