I wouldn't worry, had you been mining it, or working with it for months on end, then worry.
if you worked in conditions with exposure to fibres everyday for 20 years - then yes, you are buggered...
I don't know why people still persist with the claim that asbestos is only dangerous if there is exposure to huge amounts of it for a very long periods of time.
The Supreme Court upheld a £240,000 compensation claim by Dianne Willmore who died from malignant mesothelioma in 2009. She didn't mine the stuff nor was she exposed to it for 20 years.
"While she was a pupil in the 1970s at the newly built Bowring comprehensive school in Knowsley, she was exposed to asbestos on several occasions. Asbestos insulation ceiling tiles had been taken down and stacked in a busy corridor while electricians worked on cables in the ceiling void. Bullies took children's satchels and blazers and hid them above the ceiling tiles. And there had been vandalism in the girl's toilets, where asbestos ceiling tiles were also stacked."
In landmark ruling, Dianne Willmore wins £240,000 posthumously after exposure as a child
In the case of the OP however there is nothing to worry about imo. Even if it was asbestos cement roofing panels, and it might not have been, then you're only talking about something like 10% asbestos, and the breakage didn't occur in a confined or poorly ventilated area. Some areas of the world, such as the eastern seaboard of the United States I believe, have fairly high levels of asbestos fibres in the atmosphere, I very much doubt the OP was exposed to much higher concentrations than those living in such areas.