Trailing 2-1 from the first leg in Turin, Dortmund needed to showcase their attacking talents at Signal Iduna Park to have a chance of turning the tie around.
However, the Bundesliga side were up against it from the off thanks to Carlos Tevez's early thunderbolt, before the Argentine striker created the second for Alvaro Morata and rounded off the win in the 79th minute himself.
Perhaps more worrying for Dortmund head coach Klopp than their inability to deal with Juve's front two was the fact his side seldom troubled at the opposite end, with the hosts failing to produce a shot on target in the first half.
"We were too harmless. If you don't shoot on goal, you can't score," he said. "We can't blame the ball, because it flew fairly well, as you could see with the goal Tevez scored.
"Every minute the opponent gained in confidence and we ended up having none.
"Juve were simply better than us, but they also had the perfect start after three minutes."
Captain Mats Hummels agreed that Dortmund failed to recover from the early setback and that they never settled into a second half that Juve dominated.
"The early goal we conceded was surely a shock for us. You can't deny that," Hummels added. "For almost the entire match we failed to create any noteworthy chances.
"In the second half we completely lost our rhythm and in the end the scoreline was deserved.
"We can't claim that we were at the same level as Juventus."
