Melbourne, St Kilda, Port Adelaide and the Western Bulldogs have all been affected by the Essendon top-up scandal.
The AFL ruled that the clubs could not sign top-up players like Essendona re permitted to do, but instead could upgrade one rookie from its rookie list.
“We are disappointed,” Beveridge said on 3AW Radio on Thursday.
“I was quite passionate about the fact that we should have been able to fill the void there.
“We’ve brought in a couple of very young players as our other two (rookies). We’re not in a position to elevate another rookie for Stewart.”
Beveridge said he believes the league should have done more to help both Essendopn and the other four affected clubs move on from the doping scandal.
“For the decision to be made that they can only replace 10 of the 12 players — the strain that will put on that young group going in two less — I’d have thought it’s replace the 12 and let’s help the Bombers move on,” Beveridge said.
“Yet here we are, they’re two short and there’s four other clubs who go in short when there’s already an interesting quirk in the draw.
“There’s some clubs — and we don’t know who they are — who protested our submission that we should be able to replace players.
“That’s really just unfair that they don’t see it the same way as we do. That is because we genuinely feel for Essendon and their supporters and, in particular, the 34 players.”