Lambert was pleased with his side's fighting spirit which saw Christian Benteke hit the post with a header and go close with a shot just deflected wide.
"It was a big performance," said Lambert after the 0-0 result.
"We were missing a couple of big players. I don't think West Ham had many chances to score a goal. The lads at the back put in their heads when it mattered and blocked when it mattered and along with goalkeeper Brad Guzan I thought they were all excellent."
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