Liverpool remain three points adrift of Merseyside rivals Everton, but a massive seven behind Arsenal, having played a game more, and their European hopes are fading.
But it could have been worse for the Reds had Lucas not denied the Hammers their first win at Anfield in 50 years by turnubg James Tomkins' goalbound header off the line five minutes from time.
However, Rodgers believes his side deserve praise after dominating the Hammers for majority of the game.
"We were outstanding in terms of our game and very frustrated we didn't get the three points," he said.
"We kept pushing from the first minute but West Ham defended very well.
"In that situation, you have either got to score early or you need that wee bit of luck.
"Unfortunately when we did score it was deemed offside but when you see it again Sturridge was clearly onside."
Rodgers confirmed Stewart Downing had to be replaced after failing to recover from the illness that had threatened his participation in the first place.
It was yet another game that fell into the category Rodgers addressed in his programme notes when he stated: "From outset of this campaign, I felt it would most likely be a season of transition and there would come a few growing pains."
However, he intends to keep driving on over the remaining six games.
"Our aims are simple," said Rodgers. "We want to finish as high as we can.
"This was a game we wanted to win.
"Our form at Anfield has been getting better all the time. We love playing here.
"We are full of thrust and bodies going forward, offensively today [Sunday] we were very good."
Meanwhile, West Ham boss Sam Allardyce believes his side still require another win to secure their top-flight future.
Allardyce's team are edging themselves away from trouble and, unlike Stoke and Norwich, seem to have played themselves into a little bit of form.
"I'd like another three points," said Allardyce.
"It depends on the run of the teams below us because some are picking up two or three wins back to back. But we are looking up, not down."
Tomkins and fellow centre-half James Collins were outstanding, restricting Liverpool to few clear-cut chances, even if one of them was ruled out for offside, only for TV replays to suggest Daniel Sturridge's second-half effort should have stood.
"To have won would have been a massive bonus for us as it is 50 years since we last did it," said Allardyce.
"But it is still a very big point, and very well deserved.
"I don't think we have defended better away from home all season.
"Collins and Tomkins were really good when you consider how few chances Liverpool had."
Tomkins was not able to see out the entire game, although Allardyce revealed the calf injury that forced his early departure was not too serious.