The Eagles pushed their West Yorkshire opponents – who have now won seven on the bounce – all the way in an end-to-end contest on Sunday which saw both teams go in front twice, but a late collapse saw them surrender a second-half lead to Fax with the game finishing 28-40.
The result leaves Sheffield tenth in the Betfred Championship on points difference, yet they are just a single point from seventh spot having played a game more than Widnes and Newcastle ahead of them.
"I thought we had a real good dig,” said Aston, “I thought it was two teams that were closely matched – it could have gone either way.
"There’s eight games left of this season, if they keep performing like we have performed today there will be more wins than losses.”
Despite the disappointment of the result, Aston reserved praise for winger Ryan Millar, who scored a hat-trick of tries.
He said: “Ryan’s back to something like where he wants to be.
"He does what it says on the tin and he will finish, he’s a good player.”
York City Knights are next up for Sheffield Eagles on Sunday. They dispatched Swinton 46-10 last time out to end a six-game losing run in the league.
Aston added: "If we’re a little bit better than we were today, there’s a chance we can get the result and that’s what we’ve got to keep doing week by week, just getting a little bit better.”