The Nigerian international scored brace in the first half of the thrilling encounter.
Osimhen was, however, replaced by Dries Mertens after the break.
There were fears the striker sustained an injury which could keep him on the sidelines for a while.
The 25-year-old disclosed he had little discomfort during the game.
“I do not have a serious injury. I felt a little discomfort. I thought I should tell my coach. If I reduced the team, it would be bad. I did not want my teammates’ performance to drop. I told Mauro and the coach. That is why I left the game,” Osimhen told the club’s official website.
Galatasaray surrendered a three-goal lead to share the spoils with the visitors.
The Nigerian was happy to score his first two goals for the club but was disappointed with the outcome of the game.
“I am happy to score two goals. We are all unhappy because of the draw. We need to work hard and focus on winning the next match. I was happy with my own performance but we will work harder and try to do better in the upcoming matches.”