The England international has been supported by figures including Chelsea men's boss Maurizio Sarri, England women manager Phil Neville and the Football Association themselves.
Carney was the victim of disgusting messages that wished despicable things such as cancer and rape on her after scoring the decisive penalty in her team's 1-0 Women's Champions League clash against Fiorentina.
In response to the abuse Carney released a statement on social media: "I would like to take a moment to address the vile messages aimed at myself and my team-mates on social media this week.
"This kind of abuse is abhorrent, totally unacceptable and very upsetting. It was swiftly reported by the club as is standard practice. I now trust it will be dealt with by the correct authorities to ensure this doesn't happen again to either myself or anyone else.
"I would like to thank all those who have offered messages of support, including the fans, media and others within the game.
"I'd also like to thank Chelsea and the FA who were swift to report those responsible to both Instagram and the police.
"I'd now like to concentrate on preparing for our game against Birmingham on Sunday."