Instead they got sucker-punched when Aaron Ramsey nodded in with the visitor's first chance in the 62nd minute, inflicting a first home defeat for Dortmund by an English club.
"This was nasty, vicious," Klopp told reporters. "It feels very unfair but just have to accept it."
Dortmund, potential title contenders after a fine start to the domestic and European season, now find themselves with their backs to the wall, needing to win both of their remaining two matches to make sure of a spot in the last 16.
With two wins in their last two group games, including their 2-1 victory over Arsenal in London, Dortmund looked to be hitting the top form that carried them all the way to the final last season.
But Wednesday's setback could prove costly as they dropped to third on six points, three behind Arsenal and Napoli.
The hosts, with a perfect record in their eight home games this season, were the better team before being stunned by Arsenal's opening offensive effort.
"Football is a sport based on results. We had super moments but could not convert our chances," Klopp said. "We should have gotten more out of it."
Locked down in midfield from the start, Dortmund had trouble deploying their trademark lightning-quick breaks as they struggled to slice open a double-lined defence.
It was also a game where the skills and vision of the injured Ilkay Guendogan, out since August, were needed more than ever before.
"It hurts but we have to go on," said midfielder Nuri Sahin. "We will now focus on the game against Napoli and get three points from that."
A win against the Italians would put them level on points with them, with a game left to play.
"It is a very strong group and the positive news tonight is that with two wins we advance," Klopp said. "It's definitely going to get exciting now."
(Reporting by Karolos Grohmann. Editing by Patrick Johnston)
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