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Rossi's men failed to reach the knockout stages of the competition as they finished bottom of the so-called 'Group of Death.'
But France, Portugal and Germany all failed to reach the quarter-finals after losing their respective last-16 clashes.
Euro 2016 champions Portugal crashed out last Sunday in a 1-0 defeat to Belgium at the Estadio La Cartuja in Spain.
France, who were one of the favourites at the Euros, were dumped out on Monday after a shock penalty shootout defeat to Switzerland at the National Arena in Bucharest, Romania.
Finally, Germany made their exit from Euro 2020 on Tuesday after England secured a sensational 2-0 win at Wembley.
With all of the Group F teams out of the Euros, Rossi took to Instagram to hilariously troll Portugal captain Ronaldo, France superstar Kylian Mbappe and Germany star Manuel Neuer.
The 56-year-old Italian posted a Photoshopped image of himself on the seafront, which included Ronaldo, Mbappe and Neuer standing on the beach with luggage bags.
The Hungary head coach captioned the post: "See you on the beach!"
Hungary exceeded many fans' expectations by putting on a strong showing against Portugal, despite eventually slipping to a 3-0 defeat in their Euro 2020 opener.
Following the defeat to Portugal, Hungary bounced back to stun 2018 World Cup champions France by securing a 1-1 draw at the Puskas Arena.
Hungary were then held to a 2-2 draw by Germany in a thrilling contest at the Allianz Arena.
Rossi pulled no punches towards Ronaldo after his celebration in Portugal's win over Hungary.
He criticised Juventus superstar Ronaldo for celebrating like he had scored "in the final," saying that the five-time Ballon d'Or winner "can be annoying."
Rossi explained: "Ronaldo is a great champion but at times he can be annoying.
"After the penalty with us, he celebrated as if he had scored in the final. People notice these things."
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