Szalai injured his hand in training before Schalke's 3-2 victory at PAOK, but scored a brace to help his team qualify for the Champions League.
The player said that he is pleased that he will not spend time on the sidelines requiring surgery.
"I am very happy it's nothing worse," Bundesliga.com quotes Szalai as saying. "I really wanted to play. Missing the match was never an option."
Szalai is currently enjoying a run in the team with Klaas-Jan Huntelaar absent through injury.