The Nottinghamshire side have lost just twice in League Two this season following their promotion from the Conference Premier and currently sit fifth in the table after 10 games.
"We have high expectations and I think we can exceed the expectations of non-Mansfield fans," Radford told BBC East Midlands Today.
"I can't see us not being in the playoffs or coming first or second. I'm a really happy chairman and it's so much easier to run a club back in the Football League.
"The fans have been fantastic and I'm really happy with the manager and the squad. Everything is going right at the moment."
Mansfield face Bristol Rovers on Saturday.