The 31-year-old, who has been at St Mary's since the summer of 2014, will depart when his contract expires.
Boss Hasenhuttl said: "He was here for seven years. Like always in football, things are coming to an end.
"I think he did a good job for this club. Finally, we have to move on, like always in life, and you have to start something new, and this is what we have decided as a club and we will replace him in the summer.
"It is normal in football I think to start new things and, if we have the chance to bring somebody in in the summer in this position, a younger Ryan Bertrand if you want, that helps us with his quality or his level of performances, then we can develop this young lad and then we maybe get later an even better player."
The search for that player is already well under way, with Manchester United's Brandon Williams one of the names to be touted.
"We were very far (along) in the way that we bring somebody in so I'm sure that we will find a good solution for the summer," said Hasenhuttl.
"We don't want to discuss any person, any options we have, but there are some very good ones, they are in our financial limits, and this is important for us that we find a good package that fits us."
Hasenhuttl reiterated that one player he does not expect to leave is star striker Danny Ings, who only has a year remaining on his contract.
Ings scored twice against Crystal Palace on Tuesday on his return from a hamstring problem as Saints ended a five-match winless run.
"Strikers with his quality cost normally money that we don't have to sign them, but I am very confident that Ingsy stays the next year with us," said the Southampton boss.
On Saturday, Saints take on already-relegated Fulham, and Hasenhuttl insisted there is still plenty to play for over the last three games of the season.
"I think it was important for every player and also for the whole club that we could see us going back a little bit to our old strengths," he said.
"Turning things around in a game after a very bad start is always very good. Our last two home wins came after we first went behind by one or two goals and this definitely gives us a mental lift as we show we have the quality to turn things around now.
"And, with Ingsy back on the pitch, we are definitely a different side. I was very happy with the whole performance with the ball. I think it was the perfect opponent for us to work on this part of the game.
"We know that on Saturday it's a different one. The opponent will be more aggressive. Even though they're already relegated, I'm expecting a much more intense game than on Tuesday and we have to prepare for that now.
"I think we need a minimum two more wins in the last three games. It's important we keep on going now. That's what we should see from the first moment on that we are very, very focused. 13th position must be a goal."
Southampton could be without defender Jan Bednarek, who was forced off at half-time against Palace after taking a blow to his ankle.