For the second successive weekend Nolan scored a match-winning brace, with his double on this occasion inside the opening three minutes of the second half enough to sink Aston Villa 2-0 at Villa Park.
It has been a remarkable turnaround for midfielder Nolan who was sent off twice in four matches in early December and January.
And when you consider the energy expended by West Ham over the past week in attempting to get Carroll's dismissal overturned, this latest victory - and Nolan's display in particular - was wholly satisfying for Allardyce.
"He (Nolan) knew he had let himself down, as well as the players and the club. He was pretty down," said Allardyce.
"But he has come back with renewed vigour, proven himself and what he means to the team, as a captain and as a player.
"He is trying to put right what he did wrong after those two silly dismissals, and he has done that with four goals in these last two games.
"The two goals here showed we don't have to have an Andy Carroll to score goals."
Following Carroll's red card in last Saturday's 2-0 win over Swansea after a clash with Chico Flores, the Hammers failed with two appeals to get the three-match ban rescinded.
But first a Football Association appeal's body, and then an arbitration panel, upheld the original decision of referee Howard Webb.
Although such a process overshadowed West Ham's build-up to this game, the team were hardly affected during it as they made Villa look second rate for the first 55 minutes.
The first of Nolan's goals came after just 15 seconds of the second half with a cheeky inside flick to a low Stewart Downing cross.
The second followed two minutes and 43 seconds later as he robbed a dithering Fabian Delph just outside the area before taking the ball on into the box and stroking it crisply past Brad Guzan.
Only then did Villa stir as substitute Marc Albrighton and Christian Benteke both struck the woodwork, but it was too little too late from the home side, who have now lost eight home matches this season.
Allardyce added: "I gave the lads a bit of stick at half time about not getting the lead after so much really good attacking play, stretching the Villa defence on several occasions.
"I thought we had wasted the opportunity to take the lead and we should have done a lot better in the final third.
"So I said to the players 'don't let that bite you in the backside'. But then you don't expect to go out and score two in three minutes, as Kevin did.
"We finished Villa off at that stage, with Kevin's quality of finishing coming to the fore again."
At the final whistle a chorus of boos and jeers greeted Villa's latest miserable home performance which left boss Paul Lambert bitterly frustrated.
"The two goals were really disappointing, especially right after half-time," said Lambert. "I don't think I'd taken my seat when they played a long ball and we never dealt with it.
"Whether you're young, old, or an experienced player, you deal with it. It was just a long ball and we should have dealt with it better.
"The second goal was just a basic error, and then all of a sudden we came into life in the game. But conceding two goals is just not good enough.
"The two goals irritated me because at half-time we've gone in level, and in the second half we're attacking into our favourite end and you think something's going to happen.
"But the two goals during that two-to-three-minute spell put us on the back foot.
"They were unacceptable and you cannot defend that way at this level."