Saints won 2-0 thanks to goals from Michael Obafemi and Nathan Redmond.
"Now my Christmas is fantastic," Hasenhüttl exclaimed. "We came here with a lot of confidence after the last game at Villa and we wanted to show ourselves how far we've come.
"It was a massive difference compared to the last time we played Chelsea. We were prepared for both shapes.
"We had to change a little bit. We felt all the time that the team was really well organised and were working unbelievable against the ball. Defending the box.
"We were very brave when we had the ball. That's important against such an opponent. I think the second goal was the best example of how we can play and what we want to do.
"You could feel that today we were much calmer on the ball. We were really focussed on winning.
"I'm so happy for Reddie [Nathan Redmond] because today he was so hard working. I always tell him that the goals will come.
"The young one is surprising everyone with that goal today. Not only the goal, but he was there to help the team. That's the best Michael we can imagine."