The Saints striker had scored five goals in seven games for his club before suffering a hamstring injury at the end of December.
"My gut says we've got a good enough squad to stay in the Premier League but I'm under no illusions that in the Premier League you're given nothing. We need to perform now," the 28-year-old told Sky Sports News.
"We don't want to go to the last day of the season against Manchester City, so hopefully we can get the points we need. You can't wait on other results, you need to get the wins and that's the most important thing for us."
Austin has scored 16 goals in 45 Southampton appearances since his 2016 move from Queens Park Rangers.