The Gunners had been second best for long spells and despite an improved performance after the break, the Swans earned reward for their persistence when Spanish forward Michu struck twice on the break during the closing stages.
Wenger said: "We are in this job to turn things around, and I am confident we will [because of] the quality of the players and the spirit we have in the team. It is a good moment to stick together."
He added: "I am not so much worried about [league] places, even if that is not the place you want to be, but I believe what is important is we get the quality of our game back. Then the places change."
Wenger turned 63 last month, but insisted there were no thoughts of calling time on his Arsenal career as he looks to guide the club back to winning ways.
"You make your assessment at the end of the season, as I said many times," the Arsenal boss stressed. "I know that at the moment, you get some good news from everywhere because there is a lot of unrest everywhere.
"I believe it is a good opportunity to stick together and show we are a strong club."
"There have been three great performances, each better than the (previous) one. The team is playing with a lot of confidence," Laudrup said. "They put us under pressure for 20 minutes in the second half and you know their players can make the difference at any moment, so you can never sit easy.
"We looked in quite good shape and were only defending deep a few times."