Hong Kong's Hang Seng index closed down by over 1.5%, with property stocks falling nearly 4%.
European stocks then opened in the red.
Markets were disappointed by the small scale of rate reductions.
Key benchmarks were trimmed by just a tenth of a percentage point.
The cut to the five-year rate was smaller than markets had forecast.
Analysts at Bank of America called the cuts "marginal", and said they would do little to revive flagging growth.
The cuts came amid signs that a post-health crisis recovery is starting to stall.
That had ramped up pressure for more economic stimulus.
Now the focus turns to what further support may be offered.
China's cabinet met last Friday (June 16) to discuss that question.
Analysts expect more measures to be announced in the coming weeks, possibly including help for mortgage holders.
