Liverpool's bid for a first top-flight title in 24 years received a significant boost on Wednesday as City were held 2-2 at home by Gus Poyet's struggling side.
Merseyside rivals Everton also slumped to a surprise 3-2 defeat against Crystal Palace and Rodgers, whose side claimed a crucial 3-2 win over City on Sunday, warned his charges not to consider themselves immune from the end-of-season shock treatment.
"Last night (Wednesday) was a warning sign for everyone that at this point of the season, nothing is guaranteed," the 46-year-old, whose side are two points clear at the Premier League's summit, said.
"Our rivals may have dropped points but it's irrelevant, you've got to win your own games.
"We can use the stress as an opportunity. I think for us, it won't be the case of pressure, we may get a little bad luck or genuine honest mistake.
"The finish is still a wee bit out, we just need to focus, show the character that we have."
Next up for Liverpool is a trip to Carrow Road to face relegation-threatened Norwich City on Sunday, and Rodgers may have to do without striker Daniel Sturridge as he continues to be troubled by a hamstring injury.
"Sturridge may struggle for the weekend," he added. "It is not too serious, though he may be a risk for the weekend.
"We'll assess over the next couple of days."
