Austria, who face the Netherlands on Tuesday in their final Group D game, lost to France 1-0 but were impressive in a 3-1 win over Poland, only the second time they have scored three goals in a single European Championship finals game.
Their aggressive, front-foot style has also earned admirers.
"(Marko Arnautovic) and I recently talked about it ourselves," Rangnick said of Austria's all-time leading scorer with 36 goals who was sitting alongside at a news conference on Monday.
"When Marko heard that I'd become boss here, he thought 'ooh, this might be a bit tight now', but I didn't see it like that. I didn't quite understand why it was seen like that.
"He (Arnautovic) played from the start against Poland and possibly tomorrow as well in such an important game."
The Dutch lead the group on four points, ahead of France on goals scored, with Austria third.
Defender Gernot Trauner will not be available on Tuesday due to injury.
"He didn't train today, he's definitely out for tomorrow," Rangnick said. "And even in the next game, he won't be able to play probably. I'm really sorry for him, because has been in top form so far, both in training and in the games."
Rangnick expects a stiff challenge from the Dutch, but he knows what to expect.
"It feels like the Netherlands have played the same way since(legendary Dutch player) Johan Cruyff's days," Rangnick said. "A lot of width and a lot of height on the pitch. Who wins the second ball will be crucial."
Rangnick said he grew up idolising Cruyff, a three-times Ballon d'Or winner and big proponent of the Total Football philosophy.
"I once asked my coach to play in (Cruyff's) number 14 shirt," Rangnick said. "Back then it was unusual because you only used to have the numbers between one and 11. Similar to Franz Beckenbauer, Cruyff was someone who had a huge influence on the development of football, not just in his own country."
Rangnick was interim manager of Manchester United in 2021-22 before leaving to take over an Austrian side stinging from missing out on qualification for that year's World Cup.
An impressive Euro 2024 qualifying campaign, however, in which they finished a point behind Belgium in their group with 19 points from eight games, made them dark horses in Germany and they have so far not disappointed.