A 3-0 home loss, coupled with a 2-1 reversal in Turin, saw BVB crash out of the Champions League 5-1 on aggregate.
Klopp admitted that Carlos Tevez's goal after three minutes was a key moment in the game, but he felt that his side's inefficiency up front was a bigger contributing factor to their exit.
"We were totally lacking our punch in the final third," he told Sky Sport. "If you don't shoot you can't score. You saw it with Tevez and we didn't do that enough.
"After the first goal goal the match had no fluidity and the opponent's confidence grew every minute. It was not nice, but you can explain this easily. Juve was better than us today and had the perfect opening play."
"We were not as confident as Juve. So the early goal was a bad start. It comes down to us not being ruthless in the decisive parts of the pitch.
"We have to accept this defeat. We were worse than Juve and we have to realise tonight. We are out of the Champions League. That is not problem, it has happened to other teams at this stage."