Monchi apologised after he was involved in an incident with Roma fans at the airport as the team returned home from Portugal on Thursday, though he said it was not as bad as reported in the Italian media.
"My words were reported in an imprecise way," he said on Twitter. "It's true that there was a moment of tension, caused by the great disappointment we all experienced. I apologise to all the fans especially those who were at the airport at that time."
Porto were awarded penalty late in extra time following a video assistant referee (VAR) review which Alex Telles converted to give them a 3-1 win on the night in the last 16, second leg tie and send them through 4-3 on aggregate.
Shortly afterwards, Roma forward Patrik Schick went down under a challenge from Moussa Marega in the Porto area and the referee, who consulted the video assistant but did not review the incident himself, waved play on.
"Last year we asked for VAR in the Champions League because we got screwed in the semi-final and tonight, they've got VAR and we still get robbed," Pallotta posted on the club's official Twitter feed.
"Patrik Schick was clearly clipped in the box, VAR shows it, and nothing is given. I'm tired of this crap. I give up."
UEFA could not immediately be reached for comment.
There was no immediate comment from Roma on the future of coach Eusebio Di Francesco, who was already under pressure after a 3-0 derby defeat to Lazio on Saturday.
Di Francesco did not speak to the media after game, instead going straight to the team bus. Italian media named Claudio Ranieri, sacked one week ago by English Premier League side Fulham, as a possible replacement in case Di Francesco was fired or resigned.
(Writing by Brian Homewood, editing by Nick Mulvenney and Christian Radnedge)
