Flanagan admitted to assaulting Rachael Wall after a drunken row during a night out on Merseyside in December, before being sentenced on Wednesday.
The defender has been sentenced to 40 hours of unpaid work and handed a 12-month community order, but the Reds are set to begin further disciplinary procedures against the 25-year-old.
Liverpool FC spokesman said: “We condemn, in the strongest possible terms, the player’s actions during the events that took place resulting in this criminal conviction.
“It leaves his own reputation damaged and, through association, he has severely let down the club he had previously represented with distinction.
“We have expressed to him our disappointment and anger that he has failed to live up to the values of Liverpool Football Club, in this specific instance.
“The club has allowed the legal formalities to reach a conclusion before deciding on or implementing any internal disciplinary action. That internal process will now begin.
“The club has no further comment to make at this time.”