The Reds went into contest three points behind their opponents in the league, but goals from Glen Johnson, Cole and an own goal by James Collins were enough to secure victory for the away side.
And Cole, who was a 27th minute substitute for the injured Jose Enrique, insists that the result was more important than any personal achievement.
"It was very important for us. West Ham were three points above us, and we needed to keep doing the right things we've been doing," he told the club's official site.
"It was a great win - it's always nice to come back to your old club. I've scored a few against West Ham but never celebrated - the most important thing was getting the win.
|66/1||Liverpool are 66/1 with William Hill to win an FA Cup/Europa League double this season|
"It's a great group of young players here and we've got the right manager for them - they have done really well."
Liverpool teammate Jonjo Shelvey was also in a jovial mood following the game, after the former Blackpool loanee appeared to have scored the third goal of the game before replays revealed it to be a Collins own goal.
"I'm going to claim it!" said the 20-year-old. "The main thing was that we got the three points and we've got a few home games coming up now. We want to kick on."