The Dutch goalkeeper, who played in the 2010 World Cup Final, made his debut in the 3-0 win over Vitesse Arnhem in the Europa League this week.
And the 32-year-old, providing cover for the injured Fraser Forster, thinks Southampton are one of the most hard-working teams he featured in.
“I think (we can achieve) a lot,” he said. “The mentality of this team is really good, if I compare with other teams I have played for.
“This is a very nice team. They work really hard for every minute, every second of the game.
“Also in training, they work hard and we want to go forwards and get better. That is a really good thing so hopefully we can have a nice season like last year.”
Stekelenburg was also delighted with the performance against Vitesse on Thursday.
“I think the result is fantastic,” he said. “The first 10, 15 minutes, we didn’t control the game.
“After that, we took the initiative, scored a good goal and then a penalty.
“After that we controlled the game and in the second half. I am happy with the clean sheet and the result but we have to finish it in the second leg.”