Gus Poyet's men claimed only their second Premier League success of the season at Crystal Palace on Monday, triumphing 3-1 to climb out of the relegation zone and up to 15th.
Sunderland faced heavy criticism last month in the wake of a humiliating 8-0 defeat at Southampton.
However, Larsson feels they can be happy with their efforts should they claim three points against Everton on Sunday.
The Swede told Sunderland's official website: "I think if we win we can look at it as a good start to the season, especially with it coming before an international break because it is always nice to get a good result going into one.
"I'm enjoying the season so far and before the two results against Southampton and Arsenal [a 2-0 defeat] I thought we had a steady start, so there are a lot of positives to show that we are moving in the right direction."
Sunderland ended a 19-match winless run against Everton in April 2013, while both meetings between the teams last season were won by the away team.
"Whenever you play Everton it is a tough game but we have had some success against them lately," Larsson added.
"They were kind of a bogey team for us but during the last couple of seasons we have done okay, so touch wood we can put in another good performance and get the three points."
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