The 30-year-old scored the only goal of the game at St James' Park as the Magpies turned in another below-par display and succumbed all too tamely.
Allardyce said: "Of course it's our captain, who is our leading goalscorer, who has got us the three points.
"His instincts in the box are there for all to see. It's five goals he has got in 11 games now in the Premier League - it should be six because he had one chalked off this week (against Manchester City) that he shouldn't have done - and for a midfield player to be totalling up that sort of goal tally is fantastic from our point of view.
"That being the winner today [Sunday] is obviously satisfying for us all."
Nolan struck from close range, just as he had done so many times in the past for Newcastle, to convert Joey O'Brien's miscued shot and give the Hammers a 39th-minute lead to which they managed to cling for the remainder of the game.
Jussi Jaaskelainen had to produce fine saves to deny Yohan Cabaye and Hatem Ben Arfa among others, but he was ably supported by his defenders as the Magpies expended plenty of energy and endeavour but simply could not find the quality they needed to break the visitors down.
By contrast, Nolan and Mohamed Diame repeatedly stretched the home defence and it took a good save from Tim Krul to deny Andy Carroll his first goal in a claret and blue shirt 18 minutes from time.
The win saw the promoted Hammers climb into sixth place in the Barclays Premier League table, to the delight of Allardyce, whose time as manager at St James' ended unceremoniously.
He said: "It's a fantastic start to the season for us now, 11 games, 18 points.
"Anybody who looks at what we have done, we had some reasonably good fixtures at the start of the season - every game is difficult in the Premier League, but they were more winnable than some of the fixtures we have perhaps got now.
"But in saying that, in our last three games, we lost to Wigan away, which I didn't expect, we drew with Manchester City and now we have beaten Newcastle.
"The big boys are coming up and we are still getting points, and that's the pleasing thing for me because confidence grows and grows and grows, as you could see today.
"It was a very professional performance by the players and nobody was overawed coming here."
Opposite number Alan Pardew, whose former clubs include West Ham, was left to reflect upon a performance which was a pale imitation of the entertainment his side produced last season.
Asked if he cut put his finger on the reasons why, he said: "No, I wish I could.
"I think that's our 17th game and it's proving difficult to get any rhythm at home at the moment.
"Away from home, we have been strong and solid and dogged without really pulling up many trees. But at home, we need to perform better than we did today, for sure."
There was somehow an inevitability about either Nolan, the man who left the club during the summer of last year after they refused to sanction the long-term contract he was seeking, or £35million Carroll proving the match-winner, although Pardew was looking a little closer to home.
He said: "Defensively, we shouldn't have conceded that goal. We made a mistake on that and gave Kevin an easy opportunity."
Both sides were left counting the cost of a hard-fought game with Jonas Gutierrez, Papiss Cisse, Matt Jarvis, Yossi Benayoun and George McCartney all leaving the pitch injured and Demba Ba and Yohan Cabaye limping through to the final whistle.