Pierre-Emerick Aubameyang scored the decisive goal for the home side 10 minutes before the break, with Dortmund ultimately not needing to add to that.
They should have, though, with Marco Reus particularly culpable for wasting several good opportunities and Tuchel took note.
"We performed brilliantly for 90 minutes," Tuchel told reporters. "We won 1-0 but it should have been 4-0.
"We put in a superb display, showed great energy, defended at a really high level and our switch-play was outstanding.
"Obviously we did not manage to put the game beyond Leipzig's reach but at the same time we did not allow them a single shot on goal during the second half.
"It was a highly deserved win that leaves us feeling fantastic."
Tuchel acknowledged Reus should have done better in front of goal, though he refused to blow things out of proportion, backing the Germany international to make amends against Hertha Berlin in the DFB-Pokal on Wednesday.
"He needs to rest and recuperate," Tuchel said.
"Then he ill be among the goals again when we play Hertha on Wednesday."