Patel told reporters after the hour-long meeting in the chief minister's chamber in the state secretariat that the "meeting was good".
State Finance Minister Amit Mitra, finance secretary and home secretary were also present during the talks.
Banerjee, who is at the forefront of the anti-demonetisation protest, said that in the meeting she had expressed concern over people's hardship and "political discrimination amongst states".
Earlier, Patel attended a meeting of the RBI central board at the bank's regional office here where the TMC and CPI-M activists staged demonstration.
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"The Prime Minister, Parliament, nothing is available. No one is responding. He (Patel) is a direct man who is directly involved in all these... This is my satisfaction that at least I could express the views and explain the situation," she said.
"The RBI is a big institution. We respect it. It should not be politically misused," Banerjee said adding that though the governor did not answer anything, he had heard her.
Banerjee also asked Patel to give information on the distribution of currencies to different states on RBI's website "to maintain transparency".
On being asked if during the meeting Patel agreed that the implementation was wrong, the TMC chief said, "look, I don't think that as a government officer he (Patel) can say that but I think silence is sometimes golden".
Banerjee also said that the meeting with Patel was a "routine one" and that the appointment for it had been sought "before demonetisation was announced" by the Centre.