Two late goals gave Lazio a 2-0 Coppa Italia final win over Atalanta at the Stadio Olimpico in Rome on Wednesday.
It was the seventh time Lazio have won the trophy and their first triumph since 2013, the capital club's victory ending four years of Juventus dominance in Italy's domestic cup competition.
The victory also earned Lazio a place in the Europa League group stage for next season and was manager Simone Inzaghi's first Coppa Italia victory as coach, having won the competition as a player three times with the Rome club.
"It was a wonderful evening in front of marvellous fans," Inzaghi told Rai. "We had a great game, but also congratulations to Atalanta, as it was hard fought, the same way it was in Serie A, and this time we did well to turn the incidents our way.
"I told the lads that at times those who come off the bench are more important than the starting 11. I am satisfied, as we had a wonderful run in this Coppa Italia."
However, the game could have taken a huge turn when Marten de Roon's 25th minute shot was deflected onto the post via the outstretched arm of Lazio defender Bastos, who had earlier picked up a yellow card.
"It is a shocking incident and shameful to do this to Atalanta," Atalanta manager Gian Piero Gasperini said after being show footage of the incident. "This takes away credibility from VAR. It's also a bad sign for Italian football.
"It's incomprehensible, as of course the same clubs keep winning. Are we meant to only use VAR when it's handy? It was a penalty and a red card. This is a scandal!
"Tell me why it happened? Give me some justification, if you can?"
The match was marred by violence before kickoff when Lazio fans clashed with authorities, setting a police car on fire that forced two officers to be taken to hospital.
Atalanta, who were looking to lift the Coppa Italia for the first time since 1963, have been the story of the season in Italy, after making a surprise charge into the Champions League places in Serie A.
Lazio took the lead when Milinkovic-Savic rose to direct a header into the corner just minutes after coming off the bench.
Correa then put the result beyond doubt in stoppage time as he skipped past a defender, rounded the goalkeeper and tucked a finish in from close range.
"It's a pity, but these finals are like that," Gasperini said. "In the decisive moment, we seemed to be in better shape, but we lost the game on a corner. It's a shame."