The Bundesliga champions put Malaga to the sword in the first half of the quarter-final first leg at the Rosaleda but failed to take their chances, leaving the tie wide open ahead of Tuesday's return match in Germany.
"In this competition, with two matches in each round, we have only got the first one out of the way, nothing more," Klopp said.
"It's impossible to knock Malaga off their stride and that is the big danger," he added.
"But we managed to get a decent result against a well-organised opponent who were unruffled by our scoring chances and became more and more dangerous themselves.
"We have no injuries and no suspensions so on to the next game."
Dortmund's Germany midfielder Mario Goetze, who squandered two chances in the first half when he had only goalkeeper Willy Caballero to beat, said the team would have taken a 0-0 draw before the match.
"But the way the game panned out it's a very bitter result," he said.
"We had very clear chances, actually through me, and I should definitely have scored two goals.
"It was not my day today but I should without doubt have been able to help the team more."
Dortmund are seeking their second European crown after they won the Champions League in 1997 while Malaga are making their debut in the competition.
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