The former Chelsea player found the back of the net at Upton Park yesterday to launch the Reds' comeback, which resulted in a 3-2 win over West Ham United.
"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," Cole told the club's official website.
"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."
Cole has had an inconsistent season for the Merseyside outfit so far due to a number of injury woes.