Labbadia said that his side's poor performance defensively across both legs meant that the correct side advanced to the Europa League quarter-finals.
"When you go two goals behind so early on, then the whole concept is destroyed," Labbadia told Stuttgart's official website.
"In both games we conceded the goals too easily and didn't present ourselves well defensively. We didn't deserve to progress to the next round.
"Lazio were more uncompromising in defence and more effective going forward - that was the major difference."
Libor Kozak netted his first Lazio hat-trick in the game.