City, who had 10 shots in the first 15 minutes, added their second when Sergio Aguero sublimely lifted the ball over home goalkeeper Sergio Rico from close range.
Said Guardiola: "Tomorrow he will have a real assessment. For precaution he decided not to continue, hopefully it's nothing serious".
"But if they manage to hold off Manchester City, one of the greatest teams we've ever seen in English football, it would be an astonishing prize for a club who have not won the title since 1990".
Manchester City, meanwhile, will face a hard clash against their domestic rivals Tottenham Hotspur in pursuit of their first Champions League crown.
The game took place as the first fixture of the weekend; and on a warm sunny afternoon on the Thames, City took full advantage against a very poor Fulham side.
With the season nearing its end, both games are sure to be crackers.
Goalscorers Bernardo Silva left and Sergio Aguero celebrate against Fulham
City's progress means they could play nine games in April but Guardiola does not want to overthink the situation.
City had no need to go all out, given their battle on three fronts and inevitable post-international break ring rust, while Fulham, who continue to give an object lesson in how not to go about a Premier League season after earning promotion, were simply unequipped to lay a glove on their visitors.
City's work had been completed with the second, because nothing Fulham did in the remaining hour caused the slightest alarm for the champions.
That ushered in a better spell for the home side before City threatened again as Sterling's low cross was hacked away by Callum Chambers before Aguero could get to it.
The 2-0 scoreline flattered relegation-bound Fulham, as City completely dominated the game, and the the rhythm the Manchester club showed after the two-week global break particularly impressed Guardiola.
"So it would be a bit silly to say Tottenham would be the biggest game". "We try to help him score more goals, for him".
It drove me insane, I kept saying to him, we could miss out if we finish fourth and he was not having it, in his mind, Barcelona will beat Man Utd and it is laughable to even think of Tottenham as Champions League winners.
Lakers shut down LeBron for rest of season
In a move that was bound to happen eventually, the Los Angeles Lakers ended LeBron James' season on Sunday, the team announced. While James ultimately missed six weeks, his physical therapist recently suggested it should have been a season-ending injury .