Marsch and the expansion Major League Soccer franchise announced on the weekend they were parting company.
The team is in Italy for friendly matches with Serie A teams Bologna FC and Fiorentina, and Di Vaio and interim coach Mauro Biello spoke with reporters on a conference call Wednesday.
Di Vaio, who came to Montreal from Bologna, says the relationship with Marsch was normal and they worked well together.
He says the issue was more of a philosophical difference between management and the coach.
Biello admitted this trip is a bit of an audition for the head coaching job with the year-old franchise.
"They've asked me to be interim coach for this trip and going forward," he said.
"Obviously I'll be under evaluation in this next little while and I will try to work as hard as i can . . . and show what my qualities are and hopefully it will help me and put into consideration."
He said it was only normal for the sudden departure of their coach to have an impact on the team but he has tried to keep them focused on their next games.
"I think it's important that the team continue to stay focused. We're here for two weeks. The first thing I said to the group is you've got to focus on things you can control and that's performing and working hard on the field."