Moyes is often praised for keeping Everton competitive on a shoestring budget.
And Wenger said: "Of course I admire him but I can show you our balance over the last 16 years and you would be astonished.
"People forget we built a new stadium. We had to go through limited resources and maintained the club at the top and that we didn't have the money available.
"I accepted to stay and to do that. We are now going towards a period where we will be able to compete again financially with other clubs.
"We know that. And we knew that would happen. So let's hope we can show that in the future."