Under former Manchester United boss Rangnick, Austria's fortunes have been transformed over the past two years.
They won a group containing France and the Netherlands to reach the knockout stages in Germany and now have their sights set on a first ever Euros quarter-final.
Should they progress, Austria also have a kind draw through to the final.
A rematch with the Netherlands, who they beat 3-2 in the group stages, or Romania would await in the quarter-finals before facing England or Switzerland in the last four.
However, Rangnick said the stunning form of Spain, who thrashed Georgia 4-1 on Sunday to continue their perfect record at the tournament, showed the standards Austria have to reach.
"I said at the beginning of the tournament it is not impossible to become champion or get to the final," Rangnick said at his pre-match press conference on Monday.
"But you have to look at Spain. This is a team with incredible individual players but who also play on an incredible high technical level.
"We are realistic. There is only one way to get as far as possible which is to take care of the next match. This philosophy helped us to get to Leipzig today and this is the only way to get further in the tournament."
A former coach and sporting director of RB Leipzig, Rangnick and many of his players will be in familiar surroundings due to their connections with the Bundesliga club.
However, they are set to face a hostile crowd with Turkey's huge expat population in Germany backing their nation in numbers throughout the tournament so far.
"Turkey is a team that will play with a lot of emotion so we need the highest level of energy for our way of playing," added Rangnick.
"We also have to play with our heart because that is what it will be about tomorrow."
