The Hammers boss had words of encouragement for his key man despite his error.
Randolph has emerged as Bilic's first-choice stopper in recent weeks ahead of previous number one Adrian, feature in every Premier League game since early November.
Largely, he has been solid and dependable in between the posts for the Hammers, but he showed both ends of the scale at Anfield on Sunday.
The Republic of Ireland number one erred terribly with his side leading going into the second half, failing to hold onto a cross and allowing Divock Origi to turn home an equaliser.
However, he responded to that mistake superbly by pulling off a stunning save from Jordan Henderson's long-range strike late on to ensure that Bilic's side left Merseyside with a valuable and impressive point.
Bilic stressed that neither he nor Randolph himself are dwelling on the error, and insisted that despite the mistake his side would have been beaten were it not for the stopper's efforts.
The Hammers boss told the club's website: "Darren is more than okay. It’s the nature of the goalkeeper’s job.
"He made a mistake for the equaliser, it’s true, but before and after that he showed a great individual reaction. He was there in the moments we needed our goalkeeper.
"He showed his quality, his composure and he made a couple of great saves – that strike from Henderson was a crucial moment for us."
That draw was a good response to the hum
bling 5-1 thrashing at the hand of London rivals Arsenal in front of their own fans last weekend.
Bilic will be desperate to see his side build on that positive result by securing valuable wins over the next four games before the turn of the year.