Arteta was dismissed with 25 minutes left to play after the Spanish midfielder had opened the scoring from the penalty spot early in the second half at Selhurst Park on Saturday.
But two superb saves from Wojciech Szczesny kept Arsenal ahead and the visitors, who struggled to play with their trademark fluency in possession, eventually finished off spirited Palace when Olivier Giroud’s fifth Premier League goal of the season sealed the points in the closing minutes.
And after suffering their first defeat since the opening day of the season against Borussia Dortmund in midweek, Wenger was impressed with the way his players returned to winning ways with a run of difficult games to come including league fixtures against Liverpool and Manchester United.
“It was not a game of brilliance but efficiency and patience,” he said.
“We dealt well with the situation. We were mature, organised and didn’t become nervous. Szczesny made two great saves at an important moment of the game and eventually we got the second goal.”
In a week that saw manager Ian Holloway leave second bottom Palace after a fifth successive defeat, the hosts could consider themselves unlucky not to have earned something from this game.
Yet they did have a stroke of luck when Arteta was harshly given his marching orders for bringing down former Gunners team-mate Marouane Chamakh wide on the right flank.
However, with a League Cup tie against Chelsea to come this week, Wenger revealed he does not intend to appeal that decision.
A groin injury that forced the returning Mathieu Flamini off in the seventh minute could leave Arsenal down to the bare bones in midfield for the meeting with Jose Mourinho’s side.
Yet in line with his usual policy, Wenger will select a largely reserve team for that match.
Despite his injury worries, though, the French manager remains confident that his squad can cope with the real challenges yet to come.
“The only thing we can do is keep winning our games but we have some difficult games coming up and that will be a big test,” Wenger said.
“We are ambitious and we want to do as well as we can. It’s a good feeling (to be top), but without any massive significance
“We had an opportunity to put pressure on all the rivals and we did that.”
Holloway’s former assistant Keith Millen took charge of Palace, but he couldn’t stop the south Londoners suffering their eighth defeat in nine league matches since being promoted via the Championship play-offs last season.
Former Stoke City manager Tony Pulis remains the favourite to take over and Millen believes their performance against Arsenal showed that they still have a chance of turning things around.
“I think it’s an attractive job. We’re in a great financial position but if you look at the players today, whoever takes over will see there is something to build on,” he said.
“Whether we can get enough points to stay up we’ll have to see, but I think it’s important we get someone in as quickly as possible.
“We need someone from the outside to come in and have a look to see where we’re going wrong.”