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The Netherlands won all three matches in Group C to set up a last-16 clash with the Czech Republic at the Puskas Arena in Budapest, Hungary.
However, Frank de Boer's men were stunned on Sunday as Juventus star Matthijs de Ligt was sent off in the second half following a handball.
Goals from Tomas Holes and Patrik Schick sealed a stunning 2-0 win for the Czech Republic and knocked the Netherlands out of the competition.
Wijnaldum, who will leave Liverpool at the end of this month for Paris Saint-Germain, was appointed Netherlands captain in the absence of Virgil van Dijk.
However, the 30-year-old Dutch midfielder's performance as captain was blasted by Sneijder.
Speaking on NOS Sport (via Tribal Football), Sneijder said: "Is this our captain? You want him to catch up, but I have not seen anything of him all night. Not once."
Sneijder, who reached the World Cup final with the Netherlands in 2010, also slammed the "mediocre" Dutch team for their performance.
The former Inter Milan star hit out at the Netherlands by claiming that they had "no strong leaders in this team."
Sneijder added: "They were especially weak when they had the ball. I am surprised at how careless they were.
"It's not just Wijnaldum. Many of them fell through.
"We see no strong leaders in this team. But mainly I'm talking about Wijnaldum and Memphis Depay today. This is a very mediocre Dutch team."
De Boer, 51, has come under fierce criticism after the Netherlands' shock defeat to the Czech Republic.
When asked if he would stay on as Netherlands manager, he said at his post-match press conference: "I don't need to answer that now.
"I'm going to think about it quietly first, but right now I'm still full of emotion. This isn't the time to make decisions."
Featured Image Credit: NOS Sport/PA
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