The Hoops travel to Poland this week for the first leg of a demanding tie, with Legia confident after another win at the weekend when they defeated KS Cracovia 3-1.
Hoops boss Ronny Deila has already insisted he won't fall into the trap of taking Legia's mind games too seriously.
And Croatian midfielder Vrdoljak is sure Celtic will wilt in Warsaw because of the club's passionate supporters.
He said: "We've now managed two away wins in a row, but now we have a real challenge.
"We have a lot to prove when it comes to the Champions League because Celtic are a very dangerous opponent with a great tradition, although every team at this stage was always going to be a difficult game.
"I can't honestly talk about the strengths of the Scottish team because I simply haven't seen them play.
"But we'll be studying them closely in the next few days.
"You have to admit that to go through the league last season with only one defeat shows they are a great team.
"To qualify, we have to give everything and get a bit of luck too.
"But Celtic won't know about our fans. They are our 12th man.
"They can help us get the victory and if we can win in Warsaw, we can keep a clean sheet in Glasgow and qualify.
"We are a team that doesn't give a lot away. I think we have a great chance."