The Black Cats are currently second-bottom of the league put have put themselves with in a single point of safety thanks two back -to-back positive results against Liverpool and Manchester United.
Khazri, who scored his first goal for Sunderland since moving from Bordeaux in January in the 2-1 win over Manchester United last weekend, is confident that the side will start climbing the table if they can continue their good form.
He told the website: "It was good to score for the first time and good for my confidence, and for me to score and for us to beat Man United makes it even better.
"We played big games and we’ve showed that we’re worth more than the bottom three. It will be good to recuperate properly and work on a few things because the matches come around so quickly.
"We’ve just got to take it match-by-match and do what we need to stay in the Premier League. It’s very tight down the bottom and all we need is a good run of wins."
Khazri was one of five January signings as Sam Allardyce looked to reinforce his squad in order to enhance the club's survival bid.
That business looks to have reaped some reward already, with the club having picked up 11 points from their seven league matches in 2016.
Khazri's side do not play again competitively until a trip to West Ham United on 27 February.