The 27-year-old feels the Saddlers are well equipped to hold their own when they go head-to-head with former Premier League clubs Leeds, Norwich, Southampton and Charlton next term.
However, Mattis admits the club must make the Banks's Stadium a fortress to compete in the upper echelons of the table.
Mattis told the Birmingham Mail: "This club can achieve things and the Championship is not beyond us. That is what we have to aim for next season.
"All this small club stuff is rubbish. It is 11 vs 11 at the end of the day.
"The Bescot is a tight stadium and if we can get more people in there and liven it up a bit, teams won't like going there. If we want to do anything next season then we have to make the Banks's a really hard place to come to."