Stanley have only won twice in npower League Two since Leam Richardson was appointed as outgoing boss Paul Cook's permanent successor at the start of November.
Last weekend's 2-0 loss to Aldershot leaves the Reds four points above second-bottom AFC Wimbledon, who they host on Saturday.
"I think if you worry too much about going down and focus too much on relegation....it's not a banned word as such but it's not something that we're really considering at the moment," said Heys.
"I think Leam's got a lot of quality in the squad and he's a young manager. He's got a lot of experienced people around him.
"When you go around the club yourself, you see that people aren't particularly down.
"Obviously because we got beaten on Saturday we know we've got to pick ourselves up, we've got to win a few more games this new year and we've got a squad that's capable of doing that."
And Heys believes the status of underdogs is something that suits his club down to the ground.
"It's a kind of a 'never say die' attitude and I think we will always have that," he added.
"People write us off at the start of every season. We're always the bookies favourites to go down and we want to get away from that."