"I said to the players, 'Merry Christmas but it will not be enough if you will not improve'," the Spaniard said. "It's good to be there (in top spot in the table) but I'm telling you we have to improve our game."
Erling Haaland bagged a double while Tijjani Reijnders also scored in City's eighth successive league victory, a stretch that has seen them consistently gain ground on Arsenal.
But Guardiola, the perfectionist, was quick to point out the negatives and temper his praise.
"I'm so happy - we are in good position and close to the top of the league... but what will define the team is how we improve. Today was clear we were not in the right spots and we have to improve.
"We will be there. If they follow me, we'll be there. I know the level in this Premier League, I know Arsenal, I know the other teams, I know how tough they are. It's not enough."
City's final game of 2025 at the Etihad was markedly better than last season, when their final two home fixtures in 2024 were a 2-1 loss to Manchester United and a 1-1 draw with Everton.
The team's spirit and hunger - qualities Guardiola felt were missing last season - have returned.
"Spirit is there. Didn't have that last season - the spirit, the aggression and the hunger — all these attributes that they need," he said. "It comes from inside."
The City boss praised Haaland, whose brace gave him 104 goals in 114 league appearances, topping Cristiano Ronaldo's 103 goals in England's top flight. Haaland reached the mark in less than half the time it took Ronaldo.
"Thanks, Erling, always I have to thank him for the goals, obviously," Guardiola said.
He also praised Phil Foden and academy graduate Nico O'Reilly for their strong performances but stressed that technical sharpness remained a concern. He also lamented what he thought were not enough chances created, despite City's 19 shots to West Ham's eight.
"The way we played with the ball we have to improve - otherwise it will not be enough to arrive in March, April, to be a contender to win the title," he said.