Pochettino, who had a year left on his contract, was dismissed on Tuesday after Chelsea's sixth place finish in the Premier League.
Although Pochettino led the Blues into Europe next season thanks to a strong finish to the campaign, it was a difficult year for the former Tottenham and Paris Saint-Germain boss.
Pochettino's side were booed by their fans after several dismal performances and lost the League Cup final to a youthful Liverpool side, as well as suffering an FA Cup semi-final defeat against Manchester City.
Chelsea's chairman Todd Boehly expected better after spending over £1 billion on new signings in his two-year reign.
Pochettino is the third manager after Thomas Tuchel and Graham Potter to be axed since United States-based Boehly's consortium bought the West London club.
But he was popular with Chelsea's players, who appreciated his public support of them during their struggles and took to social media to hail him after his dismissal.
Chelsea captain Reece James, who endured an injury-hit season, posted on Instagram: "Thank you for everything boss. We had an amazing relationship from the moment we met.
"I never played as much as I would have hoped under you, which I am sorry for but also something I couldn't control. You believed in me and gave me a huge responsibility when many others doubted me."
Chelsea's leading scorer Cole Palmer hit 22 top-flight goals and provided 11 assists after joining from Manchester City in September.
The 22-year-old forward said on Instagram: "Gaffer, thank you for everything you have done for me & making my dreams come true. All the best."
Chelsea's Senegal striker Nicolas Jackson needed more support from Pochettino than most as he laboured through a disappointing first season.
"Good luck coach, wish we could stay more together but may God continue to bless you and you family," Jackson said.
"Thanks for your support and advices and making me a better player and person, wish you all the best."
Chelsea midfielder Moises Caicedo, who struggled to live up to his £115 million price tag, posted: "Mister! It was a pleasure. I wish you all the best for the future! What a person and what a coach."
Noni Madueke, the young winger who emerged towards the end of the season, wrote: "You taught me invaluable lessons both on and off the pitch. I will always be grateful. I wish you the best in the next chapter of your life."
Pochettino had said recently that it would not be the end of the world if he was sacked. His exit leaves Chelsea to embark on yet another managerial search in the turbulent Boehly era.
Chelsea, who haven't won a domestic trophy since the 2018 FA Cup, have been linked with Ipswich boss Kieran McKenna, Stuttgart manager Sebastian Hoeness, Girona chief Michel, Burnley's Vincent Kompany and former Brighton manager Roberto De Zerbi.