"It's a fantastic victory for us and a second away win," Allardyce told Sky Sports News. "With Newcastle being one of the top six boys these days after last season it put some pressure on us.
"I said to the lads, it's a great time to come here as they played midweek on Thursday in Europe and I experienced it myself at Bolton that the hardest game to win is the next one. That gave us an opportunity here today and we took the opportunity with both hands.
"It was a great performance and a great three points from us away from home, especially after losing three players through injury. I couldn't ask any more from the players today."
West Ham host Stoke City at Upton Park next Monday.