They lost Calum Chambers, Adam Lallana, Rickie Lambert, Dejan Lovren and Luke Shaw before the start of last season but silenced the doubters with a strong start and eventually earned an Europa League spot.
"That was exceptionally good, because the adaptation of most of the players -- most of the front players -- was exceptional and now in the whole organisation in the team it's a little bit different," the 52-year-old Koeman was quoted as saying by the Daily Echo.
"I'm not nervous, I'm convinced in the team and the players and we will show that in the next couple of weeks.
"I don't have any doubts about the players of those positions but it needs time, and the whole team needs the time to develop like last season," he added.
Saints lost 3-0 to Everton at the weekend and will look to bounce back in their Europa League tie against FC Midtjylland on Thursday night.
Koeman said they will be wary of the Danish champions' threat from set-pieces.
"Normally last season we were the best team in defending corner kicks," the former Ajax manager said. "They have the qualities, they have the set pieces, they have the throw-ins and, of course, we need attention in that.
"We know that they have a number two who has throw-ins like corner kicks and we need attention in that, because it is the most easy way to score a goal."
Saints midfielder Victor Wanyama, who scored for former club Celtic in their famous 2-1 victory over Barcelona, is hoping for a special European night.
"Scoring against Barcelona is good for any player, especially for me it was a really good night and one of the best moments in my career," the 23-year-old Kenyan international said.
"We don't have limits. It's game by game. Hopefully we are going to do better and we will see what happens.
"We have a lot of experience with our manager, he has been there, so I believe we can go far," Wanyama added.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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