Mark Noble scored twice as the Hammers beat their fellow newly-promoted side to climb to seventh in the Premier League table.
Despite Allardyce criticising his team's first-half performance, he has described the second-half display as "tremendous" as West Ham continued their excellent early-season form.
"We were lacklustre in the first half and couldn't find the right tempo to the game but defended well," he said.
"It was about showing more energy and desire and one we got the goal we were off and running. We were tremendous after that. Credit to the players after showing what they could do.
"Modibo Maiga came on and scored the goal of the game and it is great for the lad. After eight games, we have 14 points, and it has been a fabulous start."
West Ham return to Premier League action against Wigan Athletic next weekend, before hosting champions Manchester City.