A late goal from Kevin Grosskreutz guaranteed Dortmund's progression from Group F at the expense of Napoli, the winger netting three minutes from time after Souleymane Diawara had cancelled out Robert Lewandowski's opener.
However, Dortmund's margin of victory could have been much greater, with Lewandowski and Reus spurning glaring opportunities in the second half.
Klopp was quick to criticise his side for their profligacy.
"We've done everything right in the end but with so much wrong," he said.
"We wasted so many opportunities.
"It is now a great feeling. During the break one or two hard words were exchanged, but I only sought to motivate the team."
Match-winner Grosskreutz believes Dortmund can afford to celebrate after such a dramatic triumph.
"That was a great feeling," Grosskreutz said of the winning goal.
"We would have been out, and then I popped it in the corner.
"The team and all our fans deserve that. We can now indulge ourselves with one or two beers."
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