Ahead of Sunday's derby clash with Liverpool, Everton sit in eighth place, a point from the European places.
Moyes said, “It would hopefully get the club back to somewhere where people have more respect for it. Not a club that’s seen as having financial problems but has built a new stadium and is trying to regroup.
“I know the outcome of what it does for the support, not just here but globally, if you get European football. It’s a big thing because of the coverage of European football. It would be a big thing for us and for our owners and for the new people here to see what Everton Football Club is really like.
“It is a different club now to what it’s been over the last three or four years, however long it’s been. It has been a competitive club for most of the time I can remember. I want us to get back to that.
“We have always struggled to spend as much as a Liverpool or some of the other clubs but we’ve always tried to make ourselves competitive and I’d like to do that again.”