The Capital One Cup winners had lost their previous three matches, against West Brom, Arsenal and Tottenham, but Luke Moore's equaliser against the Canaries finally ended that run
The south Wales club had taken the lead through Michu before strikes from Robert Snodgrass and Michael Turner either side of half-time had put the Canaries ahead.
But Luke Moore's late equaliser ensured the spoils were shared and ended the Swans' run of losses, though the Danish manager felt his side perhaps should have claimed more than just a single point.
“Ending the losses is good, but it’s harder for me to answer whether I’m satisfied with one point,” said the Swansea boss to Sky Sports.
“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.
“It is one of those games where you say, ‘we could have won, we could have lost’. Maybe a point is fair. I am glad we stopped the bleeding and came back with a positive result.
“On the other hand, I feel we could have done a little more in the first 30 minutes, particularly, where we dominated completely.”
Controversy struck when Grant Holt’s stamp on Chico Flores didn’t receive even a yellow card, but Laudrup said the main issue was Flores’ fitness and not disciplining Holt.
He continued: “I don’t know how bad the stamp was. People have said to me that he carried on playing so it couldn’t have been so bad.
“I don’t know if the card should have been yellow, red or pink. The most important thing for me was that it wasn’t serious to Chico.
“He’s in a little pain right now, but he can walk. You have to remember Chico has just returned after seven weeks out because of injury.”