The Westphalians came away only with a point, allowing Bayern Munich to draw level at the top of the Bundesliga, but Klopp said his side only had themselves to blame.
"There was more in it for us," he said.
"Even this team which I fielded can play better than we did, particularly in the phase just after the break when we were too deep - that was unnecessary.
"We then regrouped and were the better team, but if Alex Esswein puts that chance in at the end, then Nurnberg would have won and we would have had to accept it, so a point's okay in the end."
Klopp was back on the bench following his sending off against Napoli in midweek for a frightening attack on the fourth official, but he said his reputation as a brutal coach is unwarranted.
"It's not the case that I attack the fourth official after every action, even if that is the impression," he told Sky.
"I don't need to be tied up, everything's fine."
After winning their first five games of the season, Wednesday's defeat to Napoli and Saturday's draw have interrupted Dortmund's flying start to the season, but goalkeeper Roman Weidenfeller says his side can have no complaints.
"We can be very happy with a point here," he said. "We had one or two chances that we could have done better with, and then we could have won it, but we didn't play the glorious pass to our strikers to get the goal."