Szalai, the Hungarian assistant coach, collapsed on the bench after falling ill, sparking an immediate response from his teammates, who formed a protective circle around him as he received medical treatment for 13 minutes.
The 36-year-old former player, who won 86 caps for his country and retired in 2023, was later hospitalised but confirmed he was doing well after the match.
Once play resumed, Weghorst stepped up to convert a penalty and celebrated with exuberance, angering a number of fans who saw his actions as insensitive given the circumstances just moments before.
Among the critics was former Dutch international Rafael van der Vaart, who didn't hold back his thoughts: "When you score and celebrate like Wout Weghorst did, it really turns my stomach.
He continued: "The Hungarian players chose to continue playing, which is commendable. We get a penalty, we score and we celebrate as if we had just won the World Cup.
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Liverpool's Ryan Gravenberch, a national teammate of Weghorst's, admitted it was a 'delicate situation' but said it was ultimately a 'personal choice' for Weghorst to celebrate.
However, Dutch manager Ronald Koeman took a more defiant stance, defending his player's actions and calling those complaining 'brainless idiots'.
Weghorst himself showed remorse after the game, admitting that he hadn't thought about the situation.
"I didn't think about that (the incident) at all, I was stressed when I shot," he said. "In hindsight, I understand the negative reactions but it (the celebration) simply reflected a relief on my part.
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"After the fact, you say to yourself that it could have been done more calmly, in a more respectful way towards them. Maybe I should have acted differently."
Despite the controversy, the Netherlands cruised to a 4-0 victory, with Szalai later reassuring fans on social media that he was recovering well: "Thanks for all the messages, I'm fine."
Weghorst has scored three goals and assisted once for Ajax in the Dutch top-flight so far this season, where he plays alongside former Liverpool captain Jordan Henderson.
The former Burnley and Manchester United forward moved from to Ajax last summer on a two-year deal after the Clarets were relegated from the Premier League.
Netherlands face Bosnia and Herzegovina on Tuesday in the final Nations League game, with the side currently in second in Group 3 of League A, behind Germany.