The Reds required a couple of Steven Gerrard penalties to see off the Hammers at Upton Park to retain their place at the top of the Premier League table in what was a hard-fought battle in east London.
After the match, Rodgers spoke of the resilience and strength his players showed to secure a ninth-straight victory in the league.
"I thought we thoroughly deserved the win and we showed great character today. It was a brilliant win for us and keeps our run going," Rodgers told Sky Sports.
"We were clearly the better team. West Ham had one shot on target, which was the goal."
As for the penalty decisions, which some have deemed as contentious, Rodgers felt his side deserved to be rewarded by referee Anthony Taylor.
"When you play against West Ham the referee will get called into more decisions because of the nature of West Ham's style - they're very physical and they ask a lot of questions," Rodgers added.
"We got a couple of decisions that I thought were penalties. The first one was clear (when James Tomkins handled the ball), the second one if you analyse it we've got the reward for our enterprise and committing bodies forward.
"The young full-back (Jon Flanagan) makes a great run, Lucas plays a wonderful pass and I think if you break it down and look at it in slow motion Jon gets a touch and goes past the keeper.
"The keeper gets a little nudge with his elbow on the ball but then as Jon's gone past him, the keeper catches his foot and he goes over."
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