The Bees rounded off the campaign with a disappointing 4-2 defeat to Newcastle United, ensuring that they had to settle for a 16th-placed finish.
Prior to the game, the Bees announced that Baptiste, Ghoddos and Goode would all leave when their contracts expire at the end of June.
Baptiste registered two goals and five assists in 78 games, but he only made 10 Premier League appearances during the 2023-24 season.
Brentford director of football Phil Giles told the club website: "We signed Shandon when we were in the Championship, when the aim was to achieve promotion to the Premier League. Shandon and Brentford have achieved that together, and he has gone on to be involved in some significant moments for us as a Premier League player for the last three seasons.
"In truth, I'm sure Shandon would want to be involved on the pitch more than he has been, which is why we feel it's the right time to let him become a regular and key player at another club."
Ghoddos, Goode depart with Baptiste
Ghoddos finds himself in a similar position after he was released by Brentford last summer, before the club brought him back on a one-year contract.
During his time with the West London side, the midfielder scored six goals and provided eight assists in 108 appearances.
"Saman is one of the nicest guys I've ever met in football," Giles said. "He's always positive and makes a fantastic contribution at training and around the squad every day.
"It was an easy decision to bring him back last summer and he has completely justified that decision. He will always be welcome at the club and of course, we shouldn't rule out him coming back again sometime in the future."
As for Goode, he has made just 20 appearances since arriving from Northampton in 2020 and has spent time out on loan at Sheffield United, Blackpool and Wigan Athletic.
Giles said: "Charlie has been incredibly unlucky with injuries and illness since not long after joining us. That said, whenever he played, I always thought he did very well and contributed to some important results, especially during our first season in the Premier League.
"He has shown that he can play at this level, and it was good to see him get some significant minutes during the latter part of the season at Wigan."
Reguilon, Maupay return to parent clubs
Brentford have also confirmed that loanees Reguilon and Maupay will return to Tottenham Hotspur and Everton respectively.
After spending the first half of the season with Manchester United, Reguilon made 16 appearances during his time with Thomas Frank's side, contributing four assists to their successful survival bid.
Maupay, who previously spent two years at Brentford, leaves after scoring eight goals and providing four assists in 34 matches during his second spell with the Bees.
"Sergio was the perfect player at the perfect time for us," Gilles added. "It was a loan that, at best, would suit both parties and that is exactly the way that it has turned out. Sergio has enjoyed being with us and played a significant number of minutes which will set him up well for next season, wherever that may be.
"Neal has made a massive contribution to Brentford during both of his spells with the club. He has completely justified the decision to bring him back on loan, contributing important goals and being a key part of the squad.
"Brentford retains the option to bring Neal back permanently if we wish, but we have explained that we will pause that decision for now, having already signed Igor Thiago from Club Brugge."
Having announced those departures, Brentford will now turn their full focus to preparations for the 2024-25 season.