Mario Balotelli scored a brace before a late Mesut Ozil penalty ensured a nervy finale.
But even though Germany were highly fancied to progress against the Azzurri, it was Prandelli's team who proved to be much the stronger side with their 2-1 win.
And yet that is not enough for the coach to believe his players have caught up with world champions Spain.
Italy drew with the Euro holders in their opening group game and beat them in a friendly last year, but Prandelli says they are still underdogs.
"The favourites are Spain because they've been working for many years and they dominate every game," said Prandelli.
"There's still a game to play, it's tiring because it's a short tournament and physical condition can play a part … We'll come up against a brilliant team who are always able to play their game and have shown that over recent years, so they're favourites."
Although he was delighted with his team, Prandelli was annoyed they failed to kill off the game in the second half despite having a number of dangerous counter-attacks.
"We were very tired in the last 10 minutes, not least because we played 120 minutes four days ago and it was a heavy pitch … We had four chances to deservedly go 3-0 up but we didn't do it and in football it only takes one episode, a free-kick or a penalty, and it can put you in difficulty."
But Prandelli said he believed it was the best performance his side has produced since he took charge two years ago, after Italy's disastrous World Cup defence in South Africa, where they crashed out in the group stages without a win.
"It's definitely the best due to the importance of the result and for three-quarters of the game we really played well," he said.
"As for the injuries we have, the doctors are trying to understand what problems there are, and there were many in the last 15 minutes.
"We'll try to get everyone back quickly, I'm sure we'll have them all [fit] but we'll come up against a team in the final that has also used up a lot of energy."
Although he insists Spain are favourites, Prandelli was keen to talk up his own side and said they are dreaming of going all the way.
"I'm proud of this team, they're really good, they're young but they're very, very strong," he added.
"We've a team with an idea that looks to implement that during the game … We have amazing players like [Andrea] Pirlo but we don't have time to eulogise about him because we know the next match is also important … When you dream, you dream big and this is only the beginning of the dream." –