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.
"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."