Cole, whose Kop career to date has been stalled by a Prem ban, showed just why he was snapped up from Chelsea as he made the most of a horror back-pass from Octavian Abduran.
He said: "There was a lot of frustration after a month without playing. It has been stop-start but I was happy to get the first goal for the team.
"The suspension seemed to last ages. I just want to get back into it now."
Cole, sent off against Arsenal in his opening game for the Merseysiders, added after firing in the fastest-ever European goal at Anfield: "It was a great start in the competition.
"You have to win your home games, so this is massive. If you win three at home and get a draw away, you're through."