The 31-year-old netted his second goal for the Reds this term in a 3-2 victory over the Hammers after returning from a season-long loan at Ligue 1 outfit Lille in the summer.
Cole has struggled with form and injuries in the current campaign, but the playmaker appears to be finally improving after Brendan Rodgers urged the England international to justify his big wages in October.
“It was a good feeling to score again and an even better one to win for our fantastic supporters,” Cole told Liverpool’s website.
“When I came off the pitch after scoring against Young Boys, considering I haven’t done much for Liverpool, the reception I got from the fans was amazing and it meant a lot to me.
“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.”