Allardyce hopes the win can provide a much-needed fillip for his relegation-threatened side.
"It was a fantastic victory for us," Allardyce said.
"It's a brilliant effort from the squad today. It's a great night for us, it's a great night for the West Ham fans, because it's twice on the trot.
"It's a victory we can enjoy tonight, but tomorrow it's up and at it again and getting ready for Manchester United.
"With a resilient performance - like we showed tonight - against Manchester United, hopefully we might get something there. Hopefully it will kick us on."
Modibo Maiga scored his first goal in more than a year and Allardyce hopes it will be the start for him, too.
"I'm delighted for him because he's showed glimpses of what we saw when we watched him in France," Allardyce added.
"All I hope is it's unlocked the door for him and he goes on to continue to score more goals."
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