The Italians could only manage a 1-1 draw in Rome which put them out 3-1 on aggregate, with Lulic saying that the damage had already been done in the away leg.
"We lost this tie in Turkey," UEFA.com quotes Lulic as saying. "We had a great attitude and we tried all we could today, taking the lead, but we didn't finish them off.
"We showed character today and we tried all we could, but it wasn't enough. It's annoying that we go out to a side no stronger than us, but we need to look ahead. We lost this game in the first leg, not tonight."
Lazio return to league action on Monday when they host Juventus.