Klopp rues missed chances
The 45-year-old coach felt his side should have converted their dominance into three points and believes they let a big opportunity slip on Saturday.
Klopp's men are now fourth and 11 points adrift of Bundesliga leaders Bayern Munich after 10 league games.
"We were not as efficient as we usually are and we did not play consistently today," Klopp told WDR2.
"It was an intense game with three clear-cut chances for us. We have to live with this draw at home and it feels like a loss. Both teams gave all they had but we deserved to win the game."
Klopp said Stuttgart were lucky not to be reduced to 10 men when midfielder Raphael Holzhauser went up for a challenge with Sebastian Kehl, who had to be substituted and has a broken nose.
"The challenge was definitely on the borderline of being a red card offence," Klopp said.