Palace looked on course to earn a hard-fought point after producing a solid defensive performance to frustrate Wenger's side at the Emirates Stadium.
However, Aaron Ramsey pounced with a 91st-minute winner to mark Arsenal's first opening-day win since 2009, and Wenger claims that the desire of his team earned them the victory.
"They made it very difficult, they defended very well and took their first opportunity," he told BBC Sport.
"After that they made it very tight, they were physically very strong and we needed to keep going. Our desire got us through."