"Kevin Nolan is a midfielder goalscorer, he's not a midfielder playmaker," Allardyce said.
"He puts himself in very dangerous positions in the box and finds the quality and the finish in the box that's basically only afforded to the top centre-forwards.
"I do think he made a difference today. The players have done terrifically well while he's been missing through suspension, but he's a big player for us and he showed that today.
"As a manager, everybody wants the big players fit and playing.
"(It was) a fantastic goal on the end of a real good performance. He showed the centre-forwards how to do it, 'This is how to score lads, come on, get your act together.'
"They still didn't learn from that because they kept missing some sitters in the second half, but the quality of the finish means that the goalkeeper got taken by surprise."
Cardiff boss Malky Mackay lamented his side's defensive display, with West Ham given chance after chance.
"I'm disappointed with the goals we lost today," Mackay said. "I'm taking nothing away from the finishes from them obviously, but the first goal was incredibly sloppy.
"Everything was very nip and tuck, it was quite tight and both teams were canceling each other out. But we lost possession in a poor area and gave away a sloppy goal and that certainly knocked our confidence at that point.
"In the second period [Peter] Whittingham hits the post and if that goes in it would change the game.
"But we tried to chase it and we lost, for us, a really uncharacteristic second goal in terms of allowing the player to come so far and be unchallenged.
"So you're up against it against a really experienced team of men, who have got a huge wage bill and can afford to bring on Carlton Cole and Gary O'Neil.
"To gift them things doesn't help, and it certainly gives you a mountain to climb."