"I experienced my first bad week in Athens. My home burgled on Wednesday and the defeat on Saturday," wrote the 32-year-old Ghana international on his Instagram account.
His Panathinaikos team had lost 1-0 at home to Xanthi on Saturday.
According to police reports, money and jewelry were taken from Essien's home in the seaside town of Varkizas in the Athens area.
"I am a survivor and looking forward to a new week. The strong will always survive," added Essien, who only joined the Greek giants in June.