The Chelsea manager rubbished claims he deliberately avoided shaking Wenger's hand after his side's 1-0 Community Shield defeat to Arsenal.
The pair have had a fractious relationship in recent years, with Mourinho labelling the Frenchman a "voyeur" and a "specialist in failure" in the past.
However, Alex Oxlade-Chamberlain's first-half strike secured Wenger his first win against Mourinho in 14 attempts.
In the aftermath of the medals being handed out, Mourinho was seen shaking Arsenal players' hands but Wenger and Mourinho notably failed to do likewise.
The issue is set to add another chapter to the relationship between the pair but Mourinho denied claims of a deliberate snub.
"I was doing what the status of my club and my status as a manager what I have to do: wait for the winners in a way where you only miss me when you want to miss me," he told reporters.
"And every Arsenal player came in my direction which was the easiest thing to do because I was right there.
"If other people didn't come in my direction it's not a story."
