Burak Yilmaz opened the scoring for the home side on 12 minutes, but Jermaine Jones' equaliser meant that honours ended even.
And with Istanbul proving a traditionally intimidating European destination, Draxler revealed the Bundesliga side's unique preparations prior to the game.
Speaking to ZDF, Draxler claimed: "We listened to the atmosphere of this stadium with a laptop, which prepared us very well. But of course, we are professionals and have to go through things like that.
"Matches are a lot of fun if 60,000 fans hiss against you, but I think we focused on the important part, delivered a good performance and built ourselves a solid foundation for the second leg."
Jones, whose strike on 45 minutes gave Schalke a valuable away goal, then gave his thoughts on the game and admitted he was content with his side's showing on the night.
"We're absolutely satisfied. We made a few mistakes, for example the goal we conceded was an invitation, but overall, we played a very good game and rightfully grabbed a point," he added.
"I think we've earned us a good amount of respect in the first half. They knew they were not able to open up the game, because it would have enabled us to finish our counters."
Schalke remain one of only three unbeaten sides in this season's Champions League and they welcome Galatasaray at the Veltins Arena for the return leg on Tuesday March 12.