The midfielder left St Mary's with an ice pack on his knee after his penalty earned Chelsea a point on the south coast.
"It's just a little knock," said Mount. "Some bruising, but nothing can stop me."
Chelsea have dropped out of the top four after West Ham beat Tottenham on Sunday but they remain unbeaten since Thomas Tuchel took over and Mount said: "A lot [of progress has been made].
"It is always difficult for a new manager to come in halfway through a season with all the games we've had.
"I feel like all the boys have adapted really well to the style we've learned under him in a short period of time. It has been going well, we have big, big games coming up now and a tough period. We need to get back to winning ways."