Taremi converted a penalty and provided two assists, including one for Arnautovic, as Inter overwhelmed the visitors and forced them into costly errors at the back.
Their success came through an energetic pressing game from Taremi in particular, with Inzaghi keen to give the pair an opportunity to start ahead of Lautaro Martinez, who came off the bench to score, and Marcus Thuram.
"The lads were good, they played a serious game against a team that came to play a purely defensive game," Inzaghi told SkySports.
"Apart from a couple of counter-attacks that we could have read better and the first five minutes of the second half, everything went well."
Inter were able to build on the 0-0 draw they earned in their Champions League opener at Manchester City.
"We wanted this victory to follow up the performance in Manchester. We have to continue in this direction. I got the answers I wanted, I'm satisfied," Inzaghi said.
He had special praise for Taremi and Arnautovic, who looked a lively pair up front.
"They are giving it their all, I have to make (selection) decisions game by game," he said. "They deserved this opportunity and took advantage of it very well.
"We have two strikers who are playing more, Thuram and Lautaro, but the season is long. Arnautovic and Taremi are two players that I wanted here (at the club).
"I am satisfied with how they work daily (in training) and they must continue like this."
