Klopp's struggling team made it three straight Bundesliga wins, climbing into 10th and four points clear of the relegation zone.
Goals from Pierre-Emerick Aubameyang, Ilkay Gundogan and Marco Reus helped Dortmund to their win.
Klopp had no doubt his side were worthy of their three points.
"I think we deserved the win today," he told a media conference afterwards.
"Looking into the statistics, we had five corners, Stuttgart two. And they scored twice from them.
"In many other moments we played really well. We tried to put a lot of pressure on our opponent. That is why many of their balls flew off of the field which didn't help them feel more comfortable.
"When your opponent isn't really self-confident in the first place you have to try that, so they don't get into the match, and we achieved this quite well."
Florian Klein's 32nd-minute penalty had drawn Stuttgart level, but Dortmund were ahead at half-time thanks to Gundogan.
Klopp said the response to the equaliser was crucial, and he rued not making more of their counter-attacking opportunities in the second half.
"The team showed a good reaction to the equaliser and it was a nice goal to make it 2-1," he said.
"In the second half, well you saw that, we had a lot of counter-attacks that we couldn't take advantage of.
"Then, on the other side, Stuttgart gave us the opportunity to score the third goal and for a change we took it.
"Then we took our foot of the pedal, and again it was a corner, a really unnecessary one I think, when we didn't defend well enough, we lost one fight for a header and after that the goal is inescapable."
