The 45-year-old coach was overcome with emotion after his side's sensational 3-2 victory over Malaga, with the Germans striking twice in injury time to win an epic encounter
The Germans appeared dead and buried when Eliseu struck to put the visitors 2-1 ahead on the night, and on aggregate, with just eight minutes remaining of an epic second-leg clash at Signal Iduna Park.
However, Marco Reus made it 2-2 in the first minute of injury time before Felipe Santana scrambled home the most sensational of late winners to spark delirium in Dortmund.
“I can't explain this,” Klopp confessed to Sky Sport. “Yet I was a witness, too! Everybody was close to a heart attack at the end! This is what football should be like, this is the most positive side of football.
“Of course, on the other hand, I feel sorry for Malaga, they gave their everything.”
Klopp conceded that his side had performed poorly for the majority of an absorbing quarter-final contest, speculating that the enormity of the occasion may have got to his players.
“For the first time this year we showed nerves,” he conceded. “We were uninspired and played without movement. Malaga defended well but, on the other hand, we were easy to defend against.
"But with this morale that we have, you have to acknowledge that we have progressed deservedly. We just put all our eggs in one basket and we kept going, even after we missed incredible chances.
“Malaga is a very good team but when we just played the ball forward somehow, it eventually worked.”
Dortmund is joined in the final four by former group rivals Real Madrid, which overcame Galatasaray 5-3 on aggregate.