Golas from Cheikhou Kouyate and Mauro Zarate were enough to see the Hammers to victory as their opponents laboured to create chances.
And Allen, who played as a forward for QPR and Charlton in the '90s, says Slaven Bilic's men surprised their hosts.
"The easy thing would be to criticise Arsenal but they were well below par, especially after seeing them win the FA Cup and the pre-season they had," Allen told BBC Radio London.
"I would use the word gutsy to describe West Ham today.
"What Slave Bilic did do was let his players do something with the ball, he didn't just set up defensively.
"West Ham had numerous chances and it was a near perfect away day performance."
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