The forward picked up the award for the second time in her Reds career after topping a supporter poll on Liverpoolfc.com.
Kapocs' closest competition in October's vote was Natalia Ramos, who earned the prize in the previous month.
The No.7 said: "It makes me feel good and I'm very happy to receive this award. It gives you a lot of confidence.
"It is special because it is voted by our supporters, who mean a lot to us."
Kapocs appeared in all four of Liverpool's matches in October, starting three of them.
She scored a 12-minute hat-trick off the bench in the Subway Players Cup defeat by Manchester United before playing a key role in the stoppage-time equaliser against London City Lionesses.
The 26-year-old continued: "It was really nice to get my first hat-trick for this club and it was even more special because I kept the ball and all the girls signed it.
"It's always important to score goals when you are an attacking player. It was a nice feeling and it gave me a boost."
**Women's Player of the Month winners 2026-27**
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**September:** Natalia Ramos
**October:** Cornelia Kapocs