The 19-year-old turned in a fine performance for the Bundesliga side and is proud of how his side coped with the intimidating Turkish crowd.
Speaking to ZDF, Draxler claimed: "We simulated the atmosphere of this stadium with a laptop, which prepared us very well. But of course, we are professionals and have 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."
Jermaine Jones was the scorer of Schalke's valuable away goal and the American midfielder feels that his team was good value for the draw.
"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 remains one of only three unbeaten sides in this season's Champions League and it will welcome Galatasaray at the Veltins Arena for the return leg on Tuesday, March 12.