The stalemate ended the Swans' three-match losing run.
Swansea dominated the opening 40 minutes and led through the otherwise wasteful Michu, only for Norwich to claw their way back into contention through Robert Snodgrass.
Michael Turner put Norwich ahead, but Luke Moore pounced to earn Swansea a point.
"Ending the losses is good, but it's harder for me to answer whether I'm satisfied with one point," Laudrup said.
"We dominated completely the first 30 minutes, we were 1-0 up and maybe should have been 2-0 up.
"We allowed them into the game out of nothing, but showed character to come back and score the second goal.
"Michu had a few chances, including the one at the end that could have been the third goal.
"Am I pleased with one point? We could have won, but we could have lost too."