Anthony Thackeray’s drop goal with under 10 seconds left on the clock made it 25-25 in an encounter low on quality after the home side had trailed for most of the match.
They got off to the worst possible start when Izaac Farrell knocked on from Whitehaven’s kick-off and the visitors crossed the line shortly after the restart with under a minute on the clock.
That set the precedent for the rest of the afternoon as far as the Eagles boss was concerned.
"It was absolute rubbish from minute one until the end,” said Aston at full-time.
"That’s no disrespect to Whitehaven, they came with a desperation, a want and a will to win the game and they should have got the win.
"We are miles away from where we were at the beginning of the season. At the moment we are hanging on.”
Despite a poor start Sheffield were soon level thanks to Greg Burns’s converted try and took the lead shorty after when Brad Knowles crossed the line.
But, after a scrappy spell, two quickfire tries from the Cumbrians put them back in front and a drop goal extended their lead to seven points at the interval.
Whitehaven added to their tally after the restart before back-to-back converted tries from Farrell and Anthony Thackeray reduced the deficit from 13 points to just one.
With Sheffield unable to force their way over the line, Thackeray kicked between the posts to salvage something from a bad day at the office.
The draw leaves Sheffield ninth in the Betfred Championship and winless in five.
"We were just all over the place,” Aston admitted.
One positive for the home side, however, was the vocal support of a small but noisy crowd who roared their team on throughout the match.
"It’s been brilliant,” Aston said of their long-awaited return.
“They might be small in numbers but they are loud in their singing. We are just disappointed that we are not where we want to be.
"When we turn up the things like we did in the first few rounds, you want to repay the fans who weren’t here to see that. We are not putting enough in.”