Liverpool enjoyed plenty of possession but were unable to break down a resilient Hammers team that came close to finding the breakthrough when Jack Collison's header was cleared off the line.
But Rodgers was left pointing to a questionable offside decision that denied Daniel Sturridge in the second half and would not criticise his players for the goalless draw that leaves them seventh.
"We obviously played very well," Rodgers told Sky Sports. "I thought some of our game today was very good.
"We had to control West Ham, coming off the back of a good result against West Brom, on the counter-attack and I thought we did that well.
"Offensively our drive and determination going forward was very good in our game. But you need the energy to keep persevering until you get the goal.
"Obviously when we did get the goal it was deemed offside and if you watch it again it was clearly onside so that was the bit of luck we needed to get the goal and open the game up.
"Unfortunately, it wasn't to be."