Nolan scored the only goal of the game as the Hammers got their return to the top flight off to a winning start against Aston Villa yesterday.
Speaking afterwards, Allardyce said: "Kevin Nolan is like David Platt because he ghosts into the box without anyone knowing how he got there.
"We might have won by more. It was a good performance with a clean sheet."
Allardyce's men next face a trip to Swansea, who began their Premier League campaign with a 5-0 thumping of Queens Park Rangers.