Southampton confirmed this week that left-back Bertrand, 31, will leave the club when his contract expires this summer.
Hasenhuttl said: "He was here for six years. Like always in football, some things come to an end.
"He's done a great job for this club. He's starting something new now. We will replace him in the summer.
"It's normal in football to start new things, and if we have the chance to bring someone in during the summer, a younger Ryan Bertrand if you like, then we will."