The Liverpool midfielder played the full game in Budapest to help his nation to a result that moved them three points clear at the top of Group G.
Hungary next face Lithuania away from home on Tuesday night, knowing a win would secure their place at next year’s final tournament.
“We need another win,” said Szoboszlai post-match. “We are looking for ourselves and we are not looking at other results. If we win in Lithuania then we are there.
“For me personally for sure it means a lot because I missed the last Euros because of my injury. So I would be really, really happy if I can play in Germany at the Euros.”