The Ferencvaros striker was knocked out after a clash with Scotland goalkeeper Angus Gunn.
Liverpool midfielder Szoboszlai admits there were major concerns amongst the players as they waited for medicos to treat their teammate.
After the Euros win, he said: "It looked bad, it was bad, it felt bad.
"I don't really know the protocols or how it works, but if our doctors say we need someone immediately to help, then I don't think they should walk.
"It's not my decision, but I think we need to change something.
"Even if someone is on the ground, and you know that it was a big collision, then just go on (the pitch).
"Even if the referee is saying don't go on, just go on. And if you can see it's nothing serious, then you can just go down and it's finished. But seconds can help a lot."