Mulgrew may start at centre-half at the Astana Arena but the Scotland international warned his Hoops colleagues about underestimating their opponents.
He told the club's website: "It's very unknown but the staff and the manager will have us well-prepared, and by the time the game comes around we will know as much as possible.
"I don't know how the travelling will affect us by the time kick-off comes around, but we've gone here very early so we will be ready in time. They will face the same journey when they come to Glasgow so I don't think we can use it as an excuse.
"It will be a hard game in difficult conditions - that's what we're expecting first and foremost. We always get asked about the plastic pitches but we've trained on it, played on it, done it all before, so hopefully we can overcome it again.
"We've got to go out there and go for the win right from the start. We'll see what they offer but we'll put up a battle and hopefully come home with a result."
Mulgrew admitted European football was high on Celtic's agenda after reaching the last-16 of the Champions League last season and he added: "Playing in Europe is huge.
"I don't think words can describe what it would mean to be involved in it. Everyone at the club wants to be involved and it would make a big difference in a lot of ways, so we're focusing on qualifying for the Champions League."