The Hammers earned a respectable 0-0 draw at Anfield, but Allardyce feels that the away outfit looked the more likely team to make the breakthrough.
"I am content, even though we should have won the game," he told BBC Sport. "We nullified Liverpool's strengths and created the better chances to score. I'm delighted. It's only the cost of our finishing that has cost us the three points.
"We know we've created better chances than Liverpool, even though they had more possession."
West Ham currently sit 12th in the Premier League table, seven points clear of the relegation zone.