His says even without talismatic Chris Conn-Clarke, those outside the club will see the strides make in recent years and tip them to be involved again.
Alty lost out in the play-off semi finals to Bromley last term, defeated by the Promotion Final winners despite a commanding first half display.
Parkinson must do it with Conn-Clarke, who clinched a record breaking move to Peterborough United in June.
He told the Non-League Paper that the Robins could even be better without the National League Player of the Year.
But he says those player brought in thanks to the cash injection could make his team more powerful all round.
He told the NLP: “We’ve bridged a bit of a gap this summer.
“You never want to lose a player like Chris but this season we will have a different way of doing things - and I do truly feel we’ll be an all-round better team for the players we’ve signed.”
He went on the say: “The fact is, Altrincham over-achieved last year and we’re probably at a level now where some people expect us to be in and around the play-offs.”
Altricnham begin their season at home to Woking on Saturday before trips south to Sutton United and Maidenhead.
Parkinson said he would love to better last season, a year which saw the club’s highest finish in almost 30 years.