Sweep the ash with a small brush, and then treat the rest of it by vacuum cleaner.
The ash is alkaline, pour some vinegar to dissolve it, and then wash it by water.
You can suck the dust if the cigarette ash can be, hair dryer can also be used. If it can not be sucked, wash part of the carpet, that's it.
Repeated several times, it will be clean. If the cigarett ash is left for a long time, then it is obvious needed be washed. If it is clean just after brushing, then the cigarett ash is new. You can stick to using a tissue dipped in water, if there is not much cigarett ash
Since it has been unable to use the vacuum cleaner, then you partially wet the carpet with a strong detergent to take a small brush carefully brush it.
