Premier League champions Chelsea have endured a season to forget, languishing in 14th position following Saturday's shock 1-0 loss at home to AFC Bournemouth.
Mourinho is facing an uncertain future with Chelsea 17 points adrift of leaders Leicester City, though the Londoners are top of Champions League Group G heading into this week's final matchday.
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"Mourinho can't live with defeat, that's why he isn't doing great," the 37-year-old told Cadena Ser.
"Despite that, I think he's the right man to turn things around at Chelsea.
"If they qualify, I think that Chelsea can go a long way in the Champions League. They aren't doing great in the Premier League, but they can knock out anyone in Europe."
Chelsea - top the standings on goal difference - host second-placed Porto in London on Wednesday, with group rivals Dynamo Kiev two points adrift.
Carvalho, who joined Chelsea from Porto in 2004 after winning the Champions League with Mourinho in Portugal, added:
"Chelsea are favourites because they're at home and only need a draw, but the smallest details decide these types of games and Porto have an outstanding team.
"I don't know if I'll support Porto or Chelsea. I grew up at Porto, but I spent more years at Chelsea. Mourinho is there and I have a lot of friends at the club."