Draxler, who played a key role in the game, said that an away draw is a good result but felt that the German side could even have won.
"We should be satisfied with what we have achieved," Bundesliga.de quotes him as saying. "Even though we had some really good chances to win. The draw does give us a good chance in the return leg.
"Maybe there was a lack of concentration, because we were well on top of the game. Perhaps that little bit of luck was missing, but Galatasaray made it very difficult for us to play."
Draxler has netted five times in 25 appearances for Schalke this season.