England or Denmark lie in wait for the Azzurri back at Wembley on Sunday after edging past La Roja in a pulsating clash under the arch on Tuesday evening.
Italy struck first as Federico Chiesa curled home a sublime effort, but Spain substitute Alvaro Morata finished a fine team move to send the match into extra time.
The match would end 1-1 after 120 minutes and had to be settled by spot-kicks, with Morata denied by Gianluigi Donnarumma before Jorginho coolly swept home to seal 4-2 shootout triumph for Mancini's men.
"First and foremost, we're delighted to have been able to provide this wonderful evening's entertainment to the Italian people," the former Manchester City boss said.
"Now we still have one more game to go and we wanted to do exactly that if possible.
"We knew it was going to be a very tough match because in terms of ball possession Spain are the best around.
"They caused us problems. We had to dig in when we needed to. We tried to score or create opportunities when we could.
"It was a very open match and of course there were some issues because we did not have too much possession.
"However, we wanted to make it into the final and we kept trying right until the end.
"As ever, penalties are a lottery but I really want to take my hat off to Spain. They're a wonderful team."
Italy have impressed throughout the Euros and stretched their unbeaten run to a jaw-dropping 33 matches, but Mancini knows they have not achieved anything yet.
"I thank the players because they believed right from day one that we could create something incredible," he said.
"We haven't done everything we need to. There's still one step to go. Now we have to rest up because this really was very challenging.
"I did say to them before the match this would be our hardest game of the competition because when you go into your sixth match in such quick succession with all the travelling that we've had to do it does become very tiring.
"We certainly struggled with Spain's ball possession, had some issues, but we wanted to make the final."
Spain shone for large spells against Italy but a lack of cutting edge proved costly for Enrique's men.
"It's not a sad night for me," the Spanish manager said. "Not at all.
"Of course there's disappointment but that's elite football. You have to be able to win and lose.
"We were very pleased to win the penalty shootout in the quarter-finals but we can't get desperate now. We have to just congratulate our opponents.
"You're always thinking about the present, thinking about being competitive.
"I said at the start we were one of the eight teams that could have won it. I don't think I was wrong about that.
"I think we now go home knowing we competed and were one of the best teams at the competition."
Enrique said he gave his players an A- grade for their tournament and threw his support behind Morata after the striker's crucial spot-kick was saved.
"Well, he has an adductor issue and it really says a lot about his personality that even despite that he wanted to take a penalty," the Spain boss said in the post-match press conference.
"He has gone through some tough times during this competition but he was brilliant.
"He really created some uncertainty within the Italy ranks so he was excellent.
"I haven't been able to see him because he's had to go to doping control, but I will go and see him now."