Allardyce saw his side waste a number of good opportunities as Swansea rode their luck in the 0-0 draw at the Liberty Stadium this afternoon.
"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," Allardyce told reporters after the game.
"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 and not difficult ones."
West Ham currently sit in 15th position in the Premier League, having won two games out of nine so far this season.