Aston's exit was due to his annoyance at what he perceived to be a "dumbing down" of the programme.
The archaeology expert, who has worked on the show for nearly two decades, allegedly did not approve of the appointment of Cambridge graduate Ochota.
Speaking to the magazine British Archaeology, Aston, the show's former site director, said: "The time had come to leave. I never made any money out of it, but a lot of my soul went into it. I feel really, really angry about it."
Ochota confirmed that there were issues between her and Aston on Time Team's Facebook page yesterday as she announced that she would also be departing the programme.
"I always loved Time Team, and was very excited to be working with Mick - he wasn't so keen!" she wrote.
Channel 4 denied that Ochota has quit, claiming that her contract was not renewed for the show's 20th anniversary series.
"Mary-Ann will not be returning for the next series of Time Team, which will be aired in 2013," said a rep for the broadcaster.
Ochota expressed disappointment in her Facebook post at the way the press had portrayed her role on the show, arguing that her former career as a model was not important.
"I'm sad about how this story has been told in the press... I was brought in to be a co-presenter, not an archaeologist, so that I could ask the questions that viewers might be asking," she said.
"The series didn't work out quite how I wanted it to either... needless to say I'm not coming back for the next series either!"
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