Substitute Sergio Floccari's injury-time winner gave the Biancocelesti a 2-1 win on the night mere moments after Arturo Vidal looked to have sent the tie into extra-time.
Although Lazio seemed to be on course for victory when midfielder Alvaro Gonzalez's diving header gave them a 53rd-minute lead, Conte thought Juventus were the better team over the course of the two legs.
"We certainly deserved better over the 180 minutes, but Lazio went through and congratulations to them," he told the club's official website.
"The last chance had a decisive bearing, because we would have qualified had it gone differently. The lads played an excellent game, but that's football and we can only take note of it."
Tuesday night's defeat means Serie A leaders Juventus have won just one of their last six matches since resuming action from the winter break.
Conte thinks his team may have turned a corner, however.
"I'm happy with how my players expressed themselves. We know exactly where we've been lacking in this recent period," added Conte, who was this week handed a two-match touchline ban as a result of his angry outburst in the wake of Saturday's draw with Genoa.