The club has been forced to postpone three 2021 Betfred Championship matches owing to outbreaks within their camp, two of which cannot be rearranged due to a lack of space in the calendar.
Aston had just 17 players available for last weekend’s win over Oldham following four more positive cases in the days leading up to the game and will once again be without the influential brothers Joel and Izaac Farrell for Sunday’s trip to Batley.
The pair are self-isolating after testing positive for coronavirus.
Playmaker Anthony Thackeray, who also missed the Roughyheads fixture, could return from an elbow injury, however.
"It’s chucked us a little bit because they are players who have been heavily involved for big parts of the season,” Aston said.
On the impact of Covid-19, he added: "It’s robbed us a little bit. The continuity, I believe, gives you consistency and we have not been consistent.
"We thought we had everybody back and this week we’ve lost, lost and lost and had a few injuries on top so it’s frustrating.
"It’s certainly had an impact on not just us, on the game for everybody. We don’t want to miss games, we train hard all week to play and love playing at weekends.”
Josh Guzdek deputised for regular goal kicker Izaac Farrel last weekend and converted all four of Sheffield’s tries.
Eighth-placed Eagles have five games left this season.
Aston said: “Once we finish hopefully we can have a few weeks off and unwind then start building for 2022.”