The 52-year-old was sacked by the defending Premier League champions in December following a 2-1 defeat by Leicester City at King Power Stadium.
They didn’t get off to a good start and the focus is on you as manager, and it’s uncomfortable
Mourinho led Chelsea to the Premier League title last season months after the west London side lifted the League Cup thanks to a 2-0 win against Tottenham Hotspur at Wembley.
Rodgers worked with Mourinho during the Portuguese’s coaches first reign at Stamford Bridge before the pair became rivals upon his return to Chelsea in June 2013.
Speaking on Goals on Sunday, former Liverpool and Swansea City manager Rodgers explained why he felt Chelsea should have stuck with Mourinho.
“Everyone looks at it and you see the success that Jose has had as a manger, but particularly last year,” Rodgers told Sky Sports.
“He signed a new contract. Clearly something wasn’t going well, if Jose goes for the success that he’s had, something is changing in football.
“I think it was just confidence. Terry, Hazard are top players and five or six months ago were winning the league comfortably. They didn’t get off to a good start and the focus is on you as manager, and it’s uncomfortable.
“I experienced it first-hand.”
Mourinho’s Chelsea side memorably halted Liverpool’s title challenge in April 2014 after a 2-0 win at Anfield prompted the Reds’s title collapse.
Chelsea played out a thrilling 3-3 draw with Everton at Stamford Bridge on Saturday evening after John Terry’s late equaliser.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news