The Black Cats moved to within three points of safety as they shattered Jose Mourinho's unbeaten record in the Premier League at Stamford Bridge.
Gus Poyet's side now know they can beat the drop if they win their remaining games this season.
Larsson told the club's official website: "We know the situation we're in, we're in desperate need of points. We've got four points from these two away games and given ourselves a chance – now we need to use it.
"We were very disappointed not to win at City, and to come from behind again today shows a lot of character and strength. This has given us a chance and hopefully we can take it."
Sunderland face Cardiff City in a crunch relegation clash next Sunday.