Given has not played for City this season but had hoped he would at least be given the goalkeeping jersey for the club's European games.
However, after seeing Hart make his first mistake of the season to gift Blackburn a goal in the Barclays Premier League on Saturday, Mancini revealed England's No 1 will start in Austria.
Mancini said: "This hasn't shaken my belief in him. Joe's a good keeper, like Shay.
"This situation can happen for a goalkeeper during the season. It doesn't change my opinion of playing Joe on Thursday."