Dortmund advanced to the quarter-final stage of the Champions League after the win which saw them go ahead 5-2 on aggregate. The defending German champions dominated the encounter at Signal Iduna Park from start to finish, with goals from Felipe Santana, Mario Gotze and Jakub Blaszczykowski sending the Bundesliga champions through to the last eight by a 5-2 aggregate scoreline.
Klopp could not hide his delight after the win which he called an 'extraordinary' moment in the club's history.
"This game ranks very high for us personally and it is an extraordinary moment," he told Uefa's official website after the game, "The entire Champions League season has been running very smoothly for us. Shakhtar showed their quality in the second half but we delivered a fantastic performance for 80 minutes in this game.
"There are plenty of teams that have been eliminated despite having performed brilliantly before and I cannot find any team that would be a dream draw for us. We are simply extremely happy about this victory and I am very proud of my team.
Neven Subotic had praise for his defensive partner Santana, who is playing in place of the injured Mats Hummels and opened the scoring for the German side.
"The first goal in a game like this is crucial. Santana is a replacement and played well and it showed that when Hummels is not there we can compensate for that. In the first half Shakhtar played a bit too safe but at the start of the second half they were really aggressive, had a couple of chances, but after that we got back to our game.
"We then created all the chances and they did not really have an answer."
Borussia Dortmund sporting director Michael Zorc was similiarly happy with the win, but urged the players to focus on their current task with a tough match against Schalke coming up.
"It was a deserved win, even if Shakhtar caused us some problems in the second half. We deserved to qualify for the next round, but we won't start thinking beyond that. We are happy about this win and now put our focus on the game against Schalke."
Chief executive Hans-Joachim Watzke added: "It's been 15 years since we were in the quarter-finals. It is about honour for us. It's good for us financially, but the feeling to reach the quarter-finals is irreplaceable."
Winger Kevin Grosskreutz claimed Dortmund's run would not end at the quarter-finals.
"We are overjoyed, everyone can be proud of themselves," he said on the club website.
"In the quarter-finals we can again achieve a great sensation."
Shakhtar coach Mircea Lucescu admitted his side were outclassed.
"Borussia deservedly progressed further," he said on the Ukrainian team's website.
"They were the team that were hard to beat. I want to note once again that it was a well-deserved victory.
"We had hope up to the 30th minute, as long as the opponents didn't create anything, with us waiting for our counter-attacking chance.
"But, unfortunately, they scored a goal from a corner kick, and then all our plans changed. There were seven fatal minutes - from the 30th to 37th when the opponents scored again after our errors."