Chasing a hopeful throughball from the visitors, Ashton got involved in a terrible mix-up in defence.
Attempting to play the ball back to Luke Daniels, he looped the ball over his helpless goalkeeper and into the empty net.
The result was harsh on a Shrewsbury side who had the best of what very few chances there were in front of a near sell-out crowd at the Prostar Stadium.
Ben Davies forced a good stop from Wayne Brown in the first half before Grant Holt fired an immediate reply against a post.
Brown again had to be at his best to deny Holt deep into injury-time, while both Simpson and opposite number Alan Knill aired different opinions after a challenge on Omer Riza by last defender and Bury captain Ben Futcher went unpunished.
But Simpson remained upbeat.
"I think it was a fantastic game of football and a goal like that didn't deserve to decide it," said the Shrews boss.
"But we said before the game that we have to make sure we're still involved at the end, and we are.
"We've got to go there on Sunday with the same determination we've shown tonight and the same spirit we've shown over the last few weeks and months and who knows what might happen?
"The game's not over, there's a hell of a lot still to play for and now we're in a situation where Bury have got something to lose."
Speaking about Ashton, Simpson added: "He's a little bit down but he's been absolutely magnificent for us lately.
"These things happen in football. On another day it might have rolled the other side of the post."
There were suggestions in the build-up to the encounter that Bury might have been downbeat due to the heartbreaking manner in which they missed out on automatic promotion on the final day by just one goal.
But they showed mettle to dent a home record that was the best in League Two this season.
Bury are now 13 games unbeaten and the bookmakers will fancy their chances of progressing to Wembley for the final on May 23.
Knill said: "It doesn't matter how you win, it really doesn't matter.
"If you work really hard then you get your rewards and I don't think anybody can say we didn't put in a shift. And we got our reward, a win, which is fantastic.
"For us to win in a play-off semi-final here is a fantastic achievement for us. Nobody expected us to win here except us.
"It's going to be another really tough game at ours but I think we're ready for it."