Porto set out needing to fight back from a 2-1 loss in Rome and they attacked from the start, taking a deserved lead in the 26th minute when Moussa Marega rolled the ball across the box for Tiquinho Soares to tap in from close range.
Porto's lead lasted barely 10 minutes as Eder Militao lunged in on Argentine Perotti, with De Rossi coolly rolling his penalty past three-time Champions League victor Iker Casillas.
Porto were awarded penalty late in extra time following a VAR review which Alex Telles converted to give them a 3-1 win on the night in the round of 16, second leg tie and send them through 4-3 on aggregate.
"The club would like to thank Eusebio for his work during his time at AS Roma and wish him success in the future".
Roma president James Pallotta claimed his side were "robbed" by VAR in their Champions League defeat to Porto, adding "I'm exhausted of this c**p".
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James, who had 27 points, eight rebounds and six assists in the loss, said he doesn't know how the team will respond should they be eliminated from playoff contention.
Di Francesco, 49, was part of the last title-winning Roma team as a player in 2001 and took over the club in the summer of 2017.
"Since returning to the club, Eusebio has always acted professionally and put the club's needs ahead of his own".
"We've got to accept it, even if the way it happened is awful to take", said De Rossi.
"Di Francesco will remain the coach who took Roma to the Champions League semi-finals after who knows how many years and he deserves credit for that".
The veteran Italian boss - who won the Premier League title with Leicester in 2016 - was sacked by Fulham last week, with the club appearing destined for the drop.
Ranieri previously managed Roma between 2009 and 2011 - leading them to a second-place finish in 2010.