Fenerbahce manager Mourinho, who managed Costa at Porto between 2002 and 2004, fought back tears and paid tribute to his former captain at a news conference before Wednesday’s Champions League third-round tie against Feyenoord.
“If he could speak with me now he would say ‘do your press conference, tomorrow play the game mister and win the game – forget about me’,” Mourinho said.
“I’m going to try and do my job today and tomorrow and then I’ll cry after.”
Costa graduated from Porto’s academy and went on to make 324 appearances for the club.
He won 24 trophies before leaving in 2005, including the Champions League, Uefa Cup and eight Primeira Liga titles.
Deco, who was also part of Porto’s Champions League-winning side said Costa was a “legendary captain” and referred to him by his nickname Bicho, which means bug in Portuguese.
“Today, Portuguese football and FC Porto lose one of its greatest symbols,” Deco posted on Instagram.
“Jorge Costa was the embodiment of Porto’s spirit and determination. A legendary captain who inspired us all.
“It was an honour to share so many titles and joys with you. Your name will forever be remembered. My condolences to the entire family. See you always, ‘Bicho’.”
Another former team-mate Pepe said: “My deepest condolences to all your family.
“Your dedication and legacy will always live in the unparalleled history of victories of FC Porto. Rest in peace, Jorge Costa.”
In 2000, Costa won the Portuguese Golden Ball – an award handed out to the league’s best player.
After falling out with Porto coach Octavio Machado, Costa joined Charlton on loan in 2001 and made 26 appearances for the Addicks.
“He was a fantastic person who always got his point across,” former Charlton boss Alan Curbishley said.
“Everyone respected him because of his ability. He was a great lad.”
Costa began his managerial career with Braga and the club said his “passing has shaken the entire national sporting community”.
“Braga cannot help but share in the enormous grief felt by his family, his friends and the entire FC Porto organisation,” the club added on X.
After stints in the dugout in Portugal with Braga, Olhanense and Academica, Costa managed teams in Romania, Cyprus, Tunisia, India and Gabon.