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After a lengthy check, though, the Italian's goal was ruled to be legal.
Neville has been vocal about some refereeing calls already this season.
Ultimately, Chiesa's goal didn't affect the final result.
Newcastle led 2-0 at the time, with Dan Burn and Alexander Isak on target, and survived what ended up being more than 10 added minutes to hold out for victory and their first major domestic trophy in 70 years.
"It was his [Dan Burn's] game," Isak told Sky Sports.
Federico Chiesa's goal was allowed to stand after a lengthy delay.
The Reds remain top of the Premier League, but the reverse at Wembley caps a painful week which also saw them eliminated from the Champions League by Paris Saint-Germain.
"The game was slow and not intense, so it’s difficult to judge for me if we were physically ready," Slot said.
"And if we play 10 times a game of football through the air against them, they win it probably nine times because they are a stronger team through the air than us, which led to the first goal and the second goal because the second goal was also a header that they won at the second post that fell for Isak and led to the 2-0."
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