The Saddlers dropped into the bottom four of League One despite not playing a game last weekend after their game at Scunthorpe was postponed due to the weather conditions.
That meant Wycombe's victory over Tranmere lifted them a point above Dean Smith's side. But Walsall have the chance to rectify that with upcoming games against Colchester, Oldham and Wycombe in the space of seven days.
"You can see there's a bit of a gap appearing but we have to go on a run and drag those teams back into it," Beevers told the Express and Star.
"You look forward to the next five games and how many points you want - regardless of how they come about. We need to push forwards and look in little blocks."
The full-back, who will be facing his former team this weekend, feels the Saddlers' position is a false one and that they have been unlucky so far.
"It's been disappointing and everyone is disappointed in where we are and what we've done. But we're a very confident bunch of lads. If you look at the first half of the season then we do feel a little hard done by."
