The 59-year-old lamented his side's inability to score before half-time, believing that his side displayed their counterattacking abilities, only for their finishing to evade them
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West Ham were looking for back-to-back Premier League away victories after beating Tottenham prior to the international break and Allardyce feels his side should have wrapped the game up before the interval.
"We should have had it over and done with by half-time," he told reporters after the clash. "We showed our classic counterattacking 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 and not difficult ones."
West Ham sit in 15th in the Premier League and will now switch their focus to Tuesday's Capital One Cup encounter at Burnley.