Marcel Schmelzer opened the scoring at Grundig-Stadion but Per Nilsson's second-half equalizer ultimately saw the visitors drop points for the first time this season.
The Schwarzgelben went into the game with a 100 percent record in the Bundesliga and took the lead through Marcel Schmelzer eight minutes before the break.
However, Per Nilsson equalized just after halftime and Dortmund, which left Robert Lewandowski, Henrikh Mkhitaryan and Nuri Sahin on the bench after their exertions in the Champions League midweek, was ultimately forced to settle for a share of the spoils.
"We did not want them to overwhelm us, so we tried to bring some freshness to the starting lineup," Klopp is quoted as saying by his club's official website. "So we are not unhappy with the point. It was an intense game with many duels.
"After the break, we had to make two changes again and we had a weaker period in which we clearly did not defend well enough. But we came back into the game well after conceding a goal and had some really great chances.
"But it was a fair result. The Bundesliga is a tough business and my team fought well today."
Up next for Dortmund is a DFB-Pokal meeting with 1860 Munich on Tuesday.