The Italian side miraculously overcame a 4-1 deficit against the Liga giants, with goals from Edin Dzeko, Daniele De Rossi and Kostas Manolas sending shockwaves across Europe.
American businessman Pallotta subsequently took to the streets with the club's fans, perhaps still refusing to believe the result.
And, in a video that has since spread like wildfire on social media, Pallotta threw himself into one of the city's ancient fountains.
Regardless of your social standing in Rome, city statutes decree that a €500 fine must be paid for wading into the water.
Mayor Virginia Raggi said: "We spoke and he apologised.
"He did it in a moment of excitement but he realises the importance of the example he needs to provide. And clearly he'll pay the fine."
Meanwhile, Roma coach Eusebio Di Francesco believes he deserves the credit for the shock win against Barcelona as he is usually blamed when his side lose.
Di Francesco opted for a change of formation - deploying a 3-4-2-1 - and he believes this was key to picking up a result, with Radja Nainggolan and Champions League debutant Patrik Schick ably supporting Dzeko.
"I take the blame for defeats and some ungrateful words on social media, so I may as well take the credit for a win," he told Mediaset Premium.
"The truth is that I made this choice to create more width, allow more counter-attacks and bring speed, but what really changed was the philosophy of the side and we have to continue like this now.
"Although we have had very good performances in Serie A, we are only now reaping the rewards – the just rewards – for the hard work we have done."