The 60-year-old was far from impressed with the Spaniard's actions in the 0-0 draw at the Stadio Olimpico on Sunday.
Despite there being no goals, Mourinho could not resist a swipe at Pedro in his post-match interview.
"I didn't want to leave [Gianluca] Mancini alone with Pedro," said the Portuguese boss, who managed Pedro in his final season at Chelsea.
"I needed [Rick] Karsdorp to stay and help him.
"Pedro is a fantastic player. But he could also be a swimmer because the way he dives in the pool is fantastic."
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Mourinho's comments certainly did not go down well with Lazio midfielder Danilo Cataldi.
"He's always the first one to talk about titles. Well, Pedro has won more titles than him," he said.
"The match? It's always difficult for me to prepare for the derby, it's so special. We all know what it means for me and for the fans."
"Today we failed to score, Rui Patricio performed a miracle, then there was the post and other opportunities. If we look at the full 90 minutes we played a good game."
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Lazio boss Maurizio Sarri also had a few words in the direction of Mourinho when being quizzed on his comments.
"I don't like dealing with Mourinho the media character, but Mourinho the person is great," the Italian said.
The draw leaves Roma in eighth with 18 points, while Lazio find themselves tenth with one point less.