Strama was promoted from the Primavera youth team in March and was given the nod to continue his work past the caretaker stage.
"We've tried to prepare for this game in the best way possible. We have great respect for Hajduk, a team that has shown themselves to be steadily growing over these early matches," said Stramaccioni in his Press conference.
"We've prepared for this match based on the current Hajduk team, which plays in a stadium that gives them a great home advantage thanks to the red-hot atmosphere.
"I know the team better as men and players. So things are very different now compared to my first match with Inter. When I was given the job in April I strongly wanted to have these responsibilities on 1 August."