Karanka, who worked as Mourinho's assistant at Real Madrid, left the Riverside Stadium by mutual consent on Thursday after four years at the club, with Steve Agnew overseeing Boro's 3-1 home loss to Manchester United.
Speaking after inflicting the struggling team's fourth successive defeat, the Portuguese claimed Karanka had previously passed up an enticing opportunity to advance his career.
"Justice for Karanka is the work he did here," Mourinho told a post-match news conference. "People cannot delete the good things we do in clubs, it doesn't matter what happens.
"I was sacked by Chelsea, people now don't like me, but nobody can go there and delete what I did. Aitor came here, 8,000 people in the stadium, almost going to League One. He keeps them in the division, goes to the play-off final, could leave, decides to stay, gets promotion.
"He could leave the club for better - I know what I'm saying - but he stays for the fans, for the owner [Steve Gibson]. He lost a good opportunity to go to a bigger club. In the end, he loses his job. It's football. I'm sure he wants this team to stay in the division. I don't think he's happy that we won."
Victory extended United's unbeaten run in the league to 18 matches and kept Mourinho's men in the hunt for UEFA Champions League qualification, which the Portuguese insists the club wants to secure via their league placing, although winning the UEFA Europa League - which would also earn passage into UEFA's top-tier continental competition - is now his priority.
"Yeah, big win, because it keeps us alive in the fourth-position race," Mourinho said. "If we don't win today then we lose a chance in relation to Arsenal's defeat, to Manchester City v Liverpool.
"I'd prefer to win the Europa League because it gives us the same, Champions League football, but it gives us a trophy, prestige, a European Super Cup. But maybe we don't win the Europa League. So we have to fight to try to finish fourth. It's a massive victory for us."
Boro caretaker Agnew meanwhile claimed not to have seen Rudy Gestede's clash with United defender Eric Bailly in the second half amid suggestions the striker may have motioned to bite his opponent.
"I didn't see anything," he told reporters. "Obviously I'm picking up that something went on but it's no concern to me."
And the temporary boss also shrugged off Mourinho's swift departure from the sidelines in the closing stages.
"[Mourinho] has done that in the past - it's hard to work out his next move. We shook hands in the tunnel."