It was Cole's first goal in the top-flight this season and followed on from his Kop end strike against Young Boys in the Europa League.
"It was a good feeling to score again and an even better one to win for our fantastic supporters," Cole told Liverpoolfc.com.
"The fans can see I want to do well for this club and it was great to score a goal for them and get the three points.
"I really do think this team is making good progression. The players are getting better and better and really responding to the things the manager wants us to do.
"It's great to play alongside the young lads with the talent and enthusiasm they have got."