Pochettino joined Chelsea ahead of the 2023-24 campaign after the club finished 12th in the previous season.
The early months of the Argentine's tenure were far from convincing as the expensively assembled squad took time to gel, but a run of five straight wins in their last five league games lifted them to sixth place and secured European football.
Former Chelsea player Craig Burley did not hold back on his assessment of Chelsea's decision, saying it displayed a lack of vision.
"It's all a bit of a mess, honestly," Burley told ESPN.
"He wasn't without fault this year, but they did finish strong. They (Chelsea) just don't have a vision, they're stumbling from one manager to the next... There's not really many managers out there right now."
Ex-Chelsea midfielder Gus Poyet said Pochettino's exit was difficult to understand, telling Sky Sports: "Everyone close to Chelsea was expecting a great summer and something important for next year.
"But we don't know the inside. I was shocked, I couldn't believe it. It was kind of impossible."
Ex-Chelsea and France defender Frank Leboeuf said Pochettino's departure had plunged the club's future into uncertainty.
"It's a pity, because they've been exceptional for the past few games, but now we don't know what we're going to face next season," Leboeuf told ESPN.
"We don't know where we'll go with all these young players. I have doubts that it'll be better than it was this season."
Chelsea's Cole Palmer, named the Premier League's young player of the season after a superb campaign, thanked Pochettino in a post on Instagram. "Thank you for everything you have done for me and making my dreams come true. All the best," Palmer said.
According to reports in British media, Ipswich Town manager Kieran McKenna, Sporting Lisbon's Ruben Amorim and ex-Brighton manager Roberto de Zerbi are among the leading candidates for the vacant managerial role at Chelsea.