Allardyce felt his team had done enough to secure all three points, and believes the lack of a clinical edge in front of goal has hindered them so far this season.
He told the BBC: "We should have had it over and done with by half-time.
"We showed our classic counter-attacking football, but unfortunately finishing qualities let us down.
"We limited Swansea to one header from a set-piece. In the second half we didn't pass it as well as in the first. It's disappointing.
"It's our fifth clean sheet in nine matches but we have only nine points in total and that's not good enough.
"If we scored in some of these matches we'd be sitting pretty. They were simple chances today and not difficult ones."
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