Luciano Spalletti's team will face Switzerland in Berlin on Saturday, giving them four days to reflect on their unconvincing efforts in Group B, where they finished second and five points behind Spain.
Italy once again failed to live up to the standard of play expected by Spalletti, an attack-minded coach who bemoaned his team's inability to retain possession and create goalscoring opportunities.
The joyous scenes that followed Zaccagni's leveller in Monday night's thrilling 1-1 draw with Croatia didn't mask the evident issues with new-look Italy who were also taught a footballing lesson by Spain.
"If you don't create, you're not going to score. You could see we were thinking about bringing a result home, without really believing that we needed a win," said Spalletti after the game.
"I expect more from my players, because they show it in flashes."
Lazio forward Zaccagni ended up under a pile of blue-shirted bodies as wild celebrations in the stands and on the pitch followed his brilliant leveller in the eighth and final minute of added time in Leipzig.
With basically no time left on the clock Zaccagni was the coolest head in the stadium as he approached Riccardo Calafiori's perfectly-weighted pass and curled home a stunning finish.
The 29-year-old's first international goal came at the end of a hugely entertaining match which looked to have been decided by Luka Modric's 55th minute strike, scored just seconds after Gianluigi Donnarumma saved his penalty.
Modric, the oldest ever scorer at a Euros, looked haunted when presented with his trophy for man-of-the-match, an award which seemed like a cruel joke after a defeat which leaves his team's hopes hanging by a thread.
Turmoil and 'venom'
"I had no idea that it was the last kick of the game when the ball came to me," said a delighted Zaccagni to Sky Sport after the game.
"Calafiori gave me such a brilliant ball for a first-time shot that I didn't even think twice about it. Then we went mad and I got battered with them all on top of me!"
Zaccagni's strike takes Italy back to Berlin where they won the World Cup in 2006 and was reminiscent of Alessandro Del Piero's winning goal in the semi-final against Germany.
Italy beat France to win the World Cup, the last hurrah for a golden generation of players which included not just Del Piero but also the likes of Andrea Pirlo, Gianluigi Buffon and Fabio Cannavaro.
"Alex (Del Piero) has always been my hero, I had his picture on my bedroom wall when I was a kid," said Zaccagni.
"We saw each other at (Italy's national training centre) Coverciano before we all left for Germany and after that we've exchanged a few messages on Instagram which for me is amazing."
Zaccagni's joy was not mirrored in Spalletti's livid post-match rant in which he turned on Italian reporters whom he accused of spitting "venom".
"I inject myself with this venom," said Spalletti, who was also angry at his tactics supposedly being leaked pre-match and claimed that "everybody" was trying to get Italy eliminated from the tournament.
Turmoil often accompanies Italy to major tournaments and the grit shown on Monday is a typical trait of a national team which is famed for its battling qualities, particularly in defence.
But performances will have to improve if Italy are to progress as Switzerland, who have a block of Serie A players, have shown themselves to be an accomplished team and England could be quarter-final opponents.
