'The Special One' arrived at Stamford Bridge in 2004 and brought immediate success, winning five trophies in three years.
But he was sacked in 2007/08 after a run of three losses, leaving his players in a state of shock.
Speaking to The Athletic, Sidwell said: "I never felt that tension or thought he was in trouble.
"There were a few games before, you could see things in the press and it really bubbled up. But you didn't feel it on the inside.
"The players were all united, no one was turning against him; he hadn't lost the dressing room.
"The day he went, I was driving my wife to the airport and the news came on the radio. I just thought, 'He's gone. What's going to happen?' We were then all called into a meeting at Cobham.
"It was awkward when Jose came to say his goodbyes. You could have heard a pin drop. It felt like someone had died.
"I called him later in the day to thank him for bringing me to Chelsea and to express regret that we didn't work together for longer.
"He told me he had no doubts I would go on to have a great career, which was nice of him. Every time I've seen him since then, through football or socially, he's been top drawer."