Brendan Rodgers is convinced if Liverpool had managed to find one goal against West Ham they could have had three or four.
The Reds' European aspirations took another blow as they were held to a 0-0 draw at Anfield.
Unless Chelsea finish outside the top four and win the FA Cup it now seems impossible for Liverpool to qualify for the Europa League.
A James Tomkins clearance off the line to deny Steven Gerrard and an incorrect call to disallow a Daniel Sturridge effort for offside were the nearest Rodgers' men came, which was frustrating for the Liverpool manager, who felt his side were clearly the better side.
"You have either got to score early on to open it up or need that wee bit of luck to get a goal," said Rodgers.
"Unfortunately when we did score it was deemed offside but when you see it again Daniel Sturridge was clearly onside.
"The performance of the players was very good. Their commitment and concentration was outstanding but we failed to get the goal that could have led to two or three more."
Rodgers confirmed winger Stewart Downing had to be replaced after failing to recover from the illness which had threatened his participation in the first place.
Liverpool remain three points adrift of Merseyside rivals Everton, but a massive seven behind fifth-placed Arsenal, having played a game more.
As for West Ham, they are now six points clear of the drop zone, although manager Sam Allardyce is not convinced survival is secure just yet.
He said: "I'd like another three points.
"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."
James Tomkins went closest for the visitors, only for Lucas to clear his header off the line five minutes from time, denying them a landmark victory.
"To have won here 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.
"James Collins and James Tomkins were really good when you consider how few chances Liverpool had."