The Hammers lost their ninth of 13 away matches this season on Sunday, after losing 2-1 to Aston Villa at Villa Park.
The former Bolton Wanderers boss believes that his side need to improve their ability in front of goal if they are to start getting results on the road.
"The away results continue to disappoint, not the form. It was an outstanding performance with nothing at the end of it," said Allardyce. "It's our own failing at the end when you don't put the ball in the back of the net.
"Before that, it only looked like one team was going to score. Even after they scored we took the game to them.
"Guzan was their hero today. We can't seem to put the ball in the back of the net. When we found what looked like a clinical finish, we got cleared of the line. That's the cruelty of the Barclays Premier League."
West Ham are 11th in the Premier League table.