Conte's Italian champions failed to break through for the one goal they needed in the second leg, as they slumped to a 0-0 draw in Turin to lose 2-1 on aggregate to the Primeira Liga champions.
Juve were eyeing a home final, with the Juventus Stadium already selected to host the Europa League decider, but Benfica held on after a controversial final period which saw both sides have non-playing men sent off.
Juventus unused substitute Mirko Vucinic and Benfica's Lazar Markovic, who had only come off in the 86th minute for Miralem Sulejmani, were banished from the technical area, after a scuffle ensued on the sidelines late in regulation time.
Striker Markovic and midfielder Enzo Perez will now miss the final, after both seeing red in the second leg.
But that was little consolation for Conte, who was fuming with his opponents' cynical mindset of time-wasting, and also took a swipe at English ref Clattenburg.
"It's a shame, as these games are right on the limit, Benfica obstructed us at every turn and the referee allowed them to do it," Conte told Sky Sport Italia.
"He (Clattenburg) gave six minutes of stoppages when we were already three in without playing, so it took us for a ride.
"It's a shame, as with two shots on target over two legs Benfica went through. Over the two games Juventus certainly deserved to go through."
Conte said his Juventus side deserved to advance to the final more than Benfica, and claimed the Portuguese outfit got lucky.
"I think Juventus gave all they had. It is an exciting, but also very exhausting season, because for the first time we've reached the final stages of European competition," Conte said.
"I don't think we saw a team struggling to stay on its feet tonight. They ran from the first to the 95th minute. It was a strong performance, we didn't get the lucky moment we needed to change the game, so in that sense Benfica were more fortunate.
"It was a real pity, as in the first leg there was a red card and penalty for the elbow on (Giorgio) Chiellini, while tonight there was an obvious penalty not given.
"The team that least deserved it went through."
