By FOX Sports Staff
The Bundesliga outfit were up against it right from the start in Thursday's defeat as they already trailed 2-0 from the first leg of this last-16 tie.
And it did not take long for the Italians to take the lead in Rome as Libor Kozak pounced on a Stefan Radu cross.
Kozak added a second not long after and although Tamas Hajnal pulled one back for Stuttgart just after the hour mark, Kozak completed his hat-trick in the 87th minute to ensure the 5-1 aggregate victory.
"We came into the game after a 2-0 first-leg defeat, where we played badly, and we came here intent on putting Lazio under pressure immediately. But after going 1-0 down - when we were caught napping - the game went downhill from there," Molinaro explained in his post-match interview.
"They are excellent in possession and it was easy for them to make it 2-0 on the counter. Lazio were far better, there is no doubt about that. Kozak scored three goals like a pure striker should - all three were beautiful goals, and credit to his team-mates who set him up - and he was ready."
Molinaro's Stuttgart team-mate Serdar Tasci added that Lazio were simply the more effective team over both legs.
"We played a decent first leg, but we conceded cheap goals and did not take our chances so it is obviously hard then to get anything from the second leg," he said.
"We have come a long way in the Europa League and I do not think many people really expected us to get this far. We started very early in the play-offs against Dinamo Moskva, then we came through the group and then beat Genk."
Thursday's game at the Stadio Olimpico in Rome was played behind closed doors following crowd trouble during their last-32 match against Borussia Monchengladbach.