Gintare Suminaite's baby was the result of a secret affair and she kept her pregnancy hidden, the Old Bailey heard.
Suminaite, of Bognor Regis, denied murder but admitted infanticide as she was mentally disturbed by giving birth. The 30-year-old had suffered significant blood loss and an injury.
Mr Justice Nicol said her circumstances were "tragic in themselves".
He sentenced Suminaite, who had spent 298 days on remand, to a 24-month community order with a rehabilitation requirement order.
"You were overwhelmed by the stress of your situation and in a state of partial denial during the pregnancy," he told her.
"At the time of giving birth you were in a state of extreme anxiety and panic."
The court heard Suminaite kept her pregnancy hidden from the authorities and her long-term partner, with whom she already had a child.
She planned to run away with her lover, a fellow Lithuanian, but did not want to be separated from her child and he went alone.
On 5 April last year, she left work early saying she had "big problems", and gave birth.
Her partner, who had been in another room in their Aldwick Road home, found her lying bleeding and pale in the bathroom surrounded by blood and a baby bath full of what appeared to be clothes.
He called an ambulance but the child lay undiscovered as medics initially did not spot the body in the baby bath.
Ambulance staff and police later returned to find the baby hidden in wet towels with a ligature around her neck, prosecutor Ed Brown QC said.
After her arrest, Suminaite said she did not know why she strangled her baby.
The court heard she had been emotionally and socially isolated during her life in England.
Her former boyfriend has cut all ties, but Suminaite remained in contact with her lover who has returned to England.
Suminaite appeared in court by videolink from Bronzefield jail.
A woman who killed her daughter shortly after giving birth in the bathroom of her West Sussex home is to walk free.