Asher-Smith is the first British woman to win a global individual sprint medal since Kathy Cook in the 200m at the 1983 World Championships.
She also won European gold at 100m in Berlin last year, as well as securing gold in the 200m and 4x100m relay.
“I wanted to come away with a medal of any colour despite all the headlines,” Asher-Smith said.
“I wanted to push myself into the top three women in the world. I didn’t think on calibre I was there yet.
“So I still needed to take it up another notch and I’m very happy to have done that.”
Asher-Smith will next race in Monday’s 200m heats, which begin at 15:05 BST.
“It’s a long season and it’s easy to get carried away in having the small achievements along the way,” Asher-Smith said of her 100m success.
“For me and my coach, it’s always been stay focused, make sure your training is tailored towards this and keep one eye on the prize.
“It’s a team effort getting me on this track and making sure I can mentally go into an event I’ve never done before and come out with a silver medal.”
