Despite taking the lead at the Emirates Stadium, the Hammers conceded four goals in the opening 10 minutes of the second half as they were crushed by their London rivals.
"I'm just stunned by what happened at the start of the second half because we were so comfortable from a defensive point of view," Allardyce told the club's official website.
"Arsenal were having a huge amount of possession, as you expect from them here, but their chances were few and far between.
"At the end of the day, when their players were flying like they were, you have got to be good in terms of your resilience at that time and we couldn't find the resilience to cope with their brilliance."
The defeat has seen West Ham slip down to 12th place in the Premier League table.