The Stags secured promotion as Conference champions last season to end a five-year exile from League Two.
Cox, who has signed six new players this summer, has revealed that he wants his team to be ambitious this season.
"I don't want to stand still, and to do that sometimes you have to raise the bar beyond what is realistic," Cox told BBC East Midlands Today.
"We will keep pushing barriers and see where it takes us. We will go in with a high level of respect, but this is a winning business - I try get it over to my players and anyone associated with the club that I want to be a winning football club.
"My heart says that we don't go into a league to finish second, but there also has to be is a sense of realism."
Mansfield face Scunthorpe United on Saturday afternoon.