Asher-Smith could only finish in fourth position in the first semi-final but her time of 22.49s proved enough for the sprinter to advance as a fastest loser.
However, last year's World Championship finalist has admitted that she will need to improve if she is to challenge for a medal.
The 20-year-old told BBC Sport: "I'm not happy with that, I know I can do much better.
"My bend was good and I think it was good until 150m, then I got into a wrong body position and it is hard to correct and makes you slow down."
Teammate Jodie Williams could only finish in eighth place in the second semi-final.