The Blues made short work of the Seagulls on Wednesday, winning 3-0 at Stamford Bridge with goals from Olivier Giroud, Eden Hazard and Ruben Loftus-Cheek.
Hudson-Odoi provided the assist for Chelsea's opening goal, finding Giroud for a close-range finish after dribbling past his defender.
It was an impressive performance from the 18-year-old winger, who earned his first league start after previously appearing six times off the bench in the Premier League.
"I am very happy for the win and we all worked hard. We had to get rhythm and bounced back well," Hudson Odoi said.
"Today we got told the team and had to prepare mentally. The manager told me to go and express myself.
"I feel comfortable, hopefully I did well."
The opportunity was seen by many as a long time coming for Hudson-Odoi, who was the subject of Bayern Munich interest in January.
Hudson-Odoi's playing time has been a topic of contention in recent months, with Maurizio Sarri routinely leaving the young winger on the bench.
But prior to the match the Italian manager reiterated that the English international is ready for the opportunity.
“It is Callum’s first Premier League start but this season he has played over 20 matches," Sarri said.
"We are trying to use him in the right way. He has improved throughout the season and now he is ready to start.”
He was not the only academy product to impress on Wednesday as Loftus-Cheek's finish signalled another solid performance from the midfielder.
And Loftus-Cheek was pleased with his own performance as he too fights for a more consistent role at Chelsea.
"We have both worked all of our lives for this chance, years of hard work and now we start in a Premier League game together. That's good for the academy."
Chelsea are set to face West Ham on Monday having moved into fifth in the Premier League with Wednesday's win.
The Blues sit level with fourth-place Arsenal, who have an extra game in hand on their London rivals.