The 35-year-old was an unused sub as Jurgen Klopp's side were beaten thanks to an 83rd-minute penalty that was converted by Ashley Barnes, a goal that ended the Reds' 68-match unbeaten run at Anfield in the Premier League.
"You'll Never Walk Alone is more important than ever right now," he wrote on Twitter.
"No good comes from feeling sorry for ourselves and excuses won't help. It's on us, all of us, to fight our way back.
"We're at our strongest when we are one force - players & supporters, TOGETHER."