The Manchester United keeper kept a clean sheet in Spain's opening two victories, a 1-0 triumph over the Czech Republic and a 3-0 defeat of Turkey but, after Croatia's two goals, he received a rating of four out of 10 from leading Spanish sports newspaper Marca.
"De Gea has lost his aura. De Gea could have done better in the two goals," Marca said. Spain finished second to Croatia in Group D.
De Gea tweeted: "Only those that lose enthusiasm are defeated. Thank you for the criticism, it motivates me. Now to continue battling."
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The 25-year-old made his senior international debut in June 2014 and was included in Spain's World Cup squad that year but did not make any appearances.
He started in only three Euro 2016 qualifiers and was not named first choice for the tournament in France until the day of Spain's opener against the Czechs.
Iker Casillas, the national team captain, had been Spain's first-choice goalkeeper since 2002.
Spain take on Italy, the team they beat 4-0 four years ago in the final, in the last 16 in Paris on Monday with De Gea expected to start.
(Reporting by Adriana Garcia, editing by Clare Lovell)
