The Danish manager says that he is happy with the character that his side showed after losing Neil Taylor to a broken ankle and Chico Flores to a red card and still earning a draw
The Welsh club's perfect start to the season looked likely to end when Steven Fletcher broke the deadlock for the away side, with Wayne Routledge levelling it for the Swans just minutes later after Neil Taylor suffered a broken ankle early on.
Fletcher struck again just before the break, with Chico Flores equalizing in the second-half to seal the draw, before the centre-back was sent off for a high challenge on Louis Saha.
"I think the game showed me a lot of good things about the character of this team," Laudrup told Sky Sports.
"In the first two games, winning five and three nil, today everything went against us.
"I think sometimes you are forced to pull out other things and I think the team showed a lot of that today.
"First the injury of Neil and we had to put on Ben Davies, a 19-year-old who did great, then there is the first mistake of the game and we go 1-0 down. We came back, but in injury-time they scored a second goal.
"We came back again in a great second half, made it 2-2 and wanted to go for the win but then a couple of minutes later we are down to 10 because of the red card of Chico.
"Even then, with one man less, we kept the ball and it was great for me to see the performance of the team today after all of these negative things.
"When I came here I knew how Swansea played but what I didn't know is what the reaction would be when they went behind and things were not going their way - our way."
Sunderland manager Martin O'Neill also expressed concern for Taylor, admitting a mistake from Gardener, who is was involved in the challenge that injured the Welsh left-back.
"[Gardener] was trying to go past and the young lad has made a foul and it's very sad he has broken his ankle," O'Neill said.
"But I think the crowd were laying into him and he was surprised by that and he came over to me to say he didn't do it.
"He was startled and he came over to tell me. We even had the free-kick, but Taylor is a very decent player and it is sad he is injured."
Gardner posted a message of concern on the social networking website Twitter: "Hope Taylor is ok I never touched him but not a nice sight when a fellow professional goes off on a stretcher."