A side tipped by many to mount a sustained challenge for the Premier League title in 2014/15 required goals in stoppage-time at the end of either half to snatch all three points at Emirates Stadium.
Brede Hangeland had nodded Palace into a surprise lead on the opening weekend, with the visitors to north London still coming to terms with the shock departure of manager Tony Pulis.
Arsenal responded positively, though, to draw level before half-time through Laurent Koscielny.
They then made their numerical advantage count in the closing stages - after Jason Puncheon had seen red - with Aaron Ramsey bundling home to secure a winning start to the season.
Asked if he felt his side were deserving victors, Wenger told Sky Sports: “We feel overall, yes.
“But credit to Palace, they fought hard – they are physically very strong, were well organised. On top of that, with the first goal, we gave ourselves a difficult task today.
“We lacked a little bit a change of pace and they gave us big problems in defending.
“We keep going and that’s one of our strengths. It paid off today.”
Pressed on where Arsenal need to improve heading forward, the Frenchman added: “The change of pace in the final third, that is usually one of our strengths and today we lacked it a little bit.
“Is it down to the quality of their defending? Is it down to the fact that we are not completely there yet physically? Maybe a bit of both.”
The one negative for Arsenal after collecting a positive result was a second-half injury suffered by full-back Kieran Gibbs, with the England international now a major doubt for Tuesday’s UEFA Champions League play-off clash with Besiktas.
Wenger added: “Certainly, if it’s a hamstring strain, yes.”
Cc1 - I'd like to see defensive cover first, personally. Somebody like Howedes would be a good signing, reliable and versatile. But a striker would be a nice addition after that.- edgar1981