By ESPNSTAR.com staff
Cole scored the crucial equaliser at Upton Park over the weekend, helping spark a comeback victory on the afternoon.
It marked his first goal in nearly 20 months and was greeted warmly by the fans after the game.
Furthermore, the win now sees the Reds just four points away from fourth place, making Champions League qualification a far more of a realistic challenge than earlier in the campaign.
Having also secured progression to the last-32 stage of the Europa League earlier in the week, Rodgers' side now have an relatively easy December set of fixtures to look forward to as they face Aston Villa, Fulham, Stoke City and Queens Park Rangers - three of whom are clubs from the bottom half of the table.
"I really do think this team is making good progress," Cole told liverpoolfc.tv.
"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.
"It was a good feeling to score again and an even better one to win for our fantastic supporters.
"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."
The former Chelsea player also hailed the performances of Jonjo Shelvey and Raheem Sterling.
Sterling helped him score his goal as the 18-year-old send in a perfect first-time pass that allowed Cole to fire a left-footed shot across the face of the goal.
“It was a great pass from Raheem for my goal,” he commented. “That’s what he’s capable of, he is a real livewire and is always a threat.
"He never stops running and working hard for the team and never looks tired, and for an 18-year-old kid that’s unbelievable.
“He is going to be a top player and he is at the right club to do that.”
Shelvey, who deputised for the suspended Luis Suarez, was also quite a handful for the West Ham defence and Cole was pleased with the midfielder's showing as well.
“Jonjo is such a clever player and he was a credit to the team.
“He worked his socks off, he held the line and he was always a threat.”
Liverpool next face Aston Villa at Anfield on Saturday in the Premier League.