Kevin Nolan scored the only goal of the game just before half-time and the Hammers held on to go sixth in the Premier League - much to the delight of their manager.
"It's a fantastic victory for us and a second away win," Allardyce told Sky Sports. "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."
Allardyce reserved particular praise for Nolan who again showed his remarkable ability to pop up with crucial goals for the Hammers.
"That's five he's got now and the enormity of Kevin's goal record for us means he's our top scorer," added Allardyce.
"Our frontmen are not really scoring at the minute but we're sharing the goals out.
"And the way he played off Andy is what I liked the most. He really does sustain the attacks by holding the possession up.
"He read the situation well in the box. It's a tap-in but you've got to be there and Kevin always seems to get in the box at the right time."