The Black Cats midfielder stressed that his side must keep control of their own destiny and not yield the initiative to Newcastle or Norwich.
The Black Cats salvaged a last-gasp draw against Stoke City on Saturday to leave them with just one defeat from their last eight league matches at the business end of the campaign.
However, they have now also won only one of their last nine, and Newcastle's recent resurgence in form has seen the Wearsiders drop below their rivals and into the relegation zone.
However, Sunderland, along with 19th-placed Norwich City, hold a game in hand over the Magpies, meaning that they still have their fate in their own hands.
Larsson, one of the club's longest-serving players with five years under his belt at the Stadium of Light, has stressed that the side must not yield that control to one of their rivals if they are to preserve their Premier League status for another year.
The Swedish international told the club's website: "We’ve done it [beaten the big teams] when we’ve really had to in previous seasons. It’s the same again and we have to go for the three points.
"There are three games left and luckily enough it is in our own hands, but we need to collect as many points as possible to make sure it remains that way.”
"It’s massive for our destiny to be in our own hands at this stage of the season, so hopefully we can get the three points on Saturday and head into the Everton game confident and pick up another win. This would set us up nicely heading into the final weekend."
Sunderland host Chelsea on Saturday before welcoming Everton to the Stadium of Light next week in their crucial game in hand ahead of a trip to Watford on the final day.