The Italians served up a 2-0 victory over the Republic of Ireland in Poznan on Monday night just when they needed it most, with their hopes of reaching the quarter-finals in serious doubt.
Goals from Antonio Cassano before the break and substitute Mario Balotelli at the death were enough to claim the points and the win, coupled with Croatia's 1-0 defeat by Spain, secured second place in Group C.
Prandelli said: "I'm happy for the team and I'm happy for the squad. I am lucky enough to work with lads who are very serious and also lads who have won a lot of trophies, and they are still very motivated.
"My task in this is not that huge because they are the ones who determine the actual team spirit.
"The players have a lot of quality. First and foremost, they really need to show intensity and then their quality will start to show itself."
Italy certainly did show their quality on the night but it was matched, for the first time in the tournament, by Ireland's battling spirit, for around 35 minutes at least.
It was then that Cassano managed to glance Andrea Pirlo's corner past goalkeeper Shay Given and although the Republic rallied once again, they had midfielder Keith Andrews sent off for a second bookable offence seconds before Balotelli made sure of the points with a last-minute volley.
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