The Reds manager believes his former side will not merely see the club as his new team any more.
Divock Origi's goal secured a 1-1 draw at Signal Iduna Park last Thursday to ensure that Klopp's men brought back a draw and a valuable away goal for the second leg at Anfield this evening.
The majority of the build-up to the match in Germany focused around Klopp's first return to the side he coached to such success for seven years until the end of last season.
That media spotlight saw the tie billed mostly as simply a meeting between the German manager's former and current teams, but after the first leg that focus has shifted to approaching the match as just a meeting of two high-quality teams.
Whilst Klopp naturally had something of an inside track on Dortmund, he suggested that his former did not know much about the Reds before the initial meeting.
However, he believes that Liverpool's strong performance away from home will have shown their opponents that they are worthy of more respect than they perhaps might have initially been given.
Klopp told liverpoolfc.com: "We have the small advantage of the away goal. In the Borussia Dortmund side, 80 per cent of their players have played together for three or four years, so we cannot be on this level, it is not possible. That is their advantage. They play a style that makes no real difference whether they play at home or away, they don’t change it.
"We knew before everything about Dortmund, but now they know more about us and that’s good because it’s a kind of respect. It’s not that they didn’t have respect before, of course, but not in this amount.
"I would say they thought, ‘good team, we know the manager’. But we showed on the pitch that it’s difficult and hard work [against us] and if they are ready for hard work, then we will be ready for hard work and it will be an intensive game – and intensive games you always can win."
Klopp's suggestion that his side have the slight advantage going into tonight's return leg is probably a fair one, with the hosts knowing that a victory or a goalless draw would send them straight through to a first European semi-final in eight years.
He rotated his squad at the weekend in the 4-1 win over Stoke City, and with his players refreshed and striker Divock Origi in lethal form with three goals in his last two games, Liverpool fans will be cautiously optimistic of completing the job at Anfield.