The Reds found themselves 3-1 down at half-time as Matip put the ball into the back of his own net after Jay Rodriguez's early brace had cancelled out Roberto Firmino's fifth-minute opener.
And while Mohamed Salah set up a tense finish after scoring 12 minutes from time, the Merseysiders were unable to complete a comeback as they crashed out at the fifth round for the third successive campaign.
"We started in front, our offensive play was okay, but in the defence we had problems," he told Liverpool's official website.
"Mistakes like my one kill every team. This mistake cannot happen, I have to clear this ball.
"In the first half, [conceding] three goals, it hurts every team. It was really hard to come back then.
"We tried [to get back] the whole time but it’s really hard against a deep-standing team. [West Brom] did what they had to do today and it was enough.
"We have to do everything to turn things [around], to get in better shape and get better results."