Teenage England star Hudson-Odoi celebrated his full Premier League debut as he kick-started Chelsea's win when teeing up Olivier Giroud.
Eden Hazard and Loftus-Cheek then dispatched fine second-half goals to push Chelsea up to fifth, but one point off Tottenham in third.
Chelsea want to tie Hudson-Odoi down to a new long-term contract by the end of the summer, with the 18-year-old still interesting a host of top European suitors.
Asked if Hudson-Odoi and Loftus-Cheek can become the bedrock of Chelsea's future, Sarri said: "I hope so, I think so and I hope so. 'At the moment very important but their potential is higher. So in the future they can become top players; for this team the future could be good."
The former Napoli manager has been well aware of the fans' frustration at Hudson-Odoi's wait for his league bow, but now the Chelsea chief believes the fast-improving star is ready to face anyone.
"Callum now is ready to play in every match, even the most difficult match," said Sarri. "He has improved a lot during the season. I was sure about his performance and he played very well.
"Callum is happy but I told him that he missed a very easy goal in the first half, and to that he just smiled. He's a good boy.
"He has to keep his feet on the ground. He could risk thinking he is a player at 100 per cent, but it's impossible to be at the top when you are 18."