New Hoops boss Ronny Deila has started putting his squad through their paces in Austria as the countdown continues to the second qualifying round clash with KR Reykjavik.
Deila will see his squad in action for the first time when they face Krasnodar on Thursday and Mulgrew said: "A lot of things are still the same, there are a lot of the same staff.
"Obviously there are one or two things needing tweaked but everyone is responding well to his ideas and it is going well."
He added: "It is always good when the matches come and you can start getting your match fitness. That is where you get most of your sharpness from so that is what we are looking towards and looking forward to."
Despite reaching the group stage for two successive seasons, Celtic once again face a treacherous European path.
The Hoops must emerge through three qualifying rounds and Mulgrew is determined there will be no slip-ups against the Icelanders.
He said: "We know what these games are like. We might not know a lot about the opposition but we know that they are into their season and everybody is fighting to get into the Champions League.
"We have done it in the last two years and we will be looking to do it again."
If Celtic are to book their place amongst Europe's elite once again, they will need big performances once again from strike star Kris Commons.
And Mulgrew has backed the forward to replicate his superb scoring form from last term.
He said: "He won us a lot of games and I am sure he is really happy with it.
"But, I know the type of player Kris and the type of person he is, and he will want to do even better again and I am sure he will be working towards that and looking to score even more goals."