A drab game saw both sides struggle to create chances, with Dortmund choosing to leave top scorer Pierre-Emerick Aubameyang on the bench on the back of the striker's recent involvement in the Africa Cup of Nations.
Despite their lack of incisiveness in the final third, Klopp claimed that there were still plenty of positives to take from the game.
He told the club's official website: "It was not perfect, but we have taken what was needed and had a really good start to the second half.
"The stability was there and if we had played the odd ball clear, it would have been even better."
Klopp was not worried by the style of football played by his team, hinting that the increasingly real worry of relegation may be having an effect on their approach to games.
He said: "One cannot speak of a relegation battle and demand champagne football.
"The result here [in Leverkusen] was absolutely fine and a point here is always strong."
One of the game's few talking points involved Leverkusen goalkeeper Bernd Leno, who was arguably lucky to stay on the pitch after appearing to handle outside his area just before the quarter-hour mark.
However, Klopp refused to criticise the performance of referee Knut Kircher, choosing instead to focus on his side's showing at the BayArena
"A free-kick [for the Leno incident] would not have been so bad. For such an intense game, there were few contentious decisions overall.
"We wanted to play a pressing game. There were two occasions where we were running up alone on goal, when should have played in more detail.
"In confined spaces, the timing has to be perfect. We have not sought perfection today, but stability."
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