Dortmund are unbeaten in their 10 league matches under Stoger, with Marco Reus on target for the third Bundesliga game in a row to cancel out an opening goal by Jean-Kevin Augustin.
Dropping two points means Dortmund missed the chance to move back to second, above Schalke, but Stoger reiterated finishing in the top four is the club's goal.
"We did not lose for the 10th game," Stoger said. "I can handle the criticism.
"The Champions League is our clear target, we're in good shape and it was clear from the start that it will be difficult here.
"We could have dealt with some situations better, we had some minor problems.
"[Roman] Burki cannot be criticised for conceding, he has also kept us in the game very well.
"What we set out to do was play very well, but we also had to be careful because Leipzig were very dangerous.
"I have seen an exceptionally good Bundesliga match and we are pretty happy to go home with a point."
Leipzig coach Ralph Hasenhuttl also felt 1-1 was a fair scoreline, with both clubs remaining in the hunt for Champions League qualification.
"Against a direct competitor, three points would have been good," Hasenhuttl said.
"The first half was high class, then it was a little worse. At the end, the 1-1 is ok.
"We still had chances to win the game, we needed to play the last pass better.
"Nothing will change until the end of the season, five teams are playing for the Champions League."