The Juve fans took the opportunity to dig at Mourinho in the closing stages of their side's 1-0 win over the Red Devils - a game dominated by the visitors - singing a colourful array of songs.
Mourinho, though, replied in kind, holding up three fingers to remind the supporters that he beat Juve across the board when he was managing in Italy.
"They are not in love with me, the hardest time for them was our treble," he told reporters afterwards.
"For players and technical staff, [head coach Massimiliano] Allegri and [chairman Andrea] Agnelli, I have total respect: they are super polite and friendly."
Mourinho also held up three fingers during United's 2-2 draw with Chelsea in the Premier League at the weekend.
That, of course, was in reference to the league titles Mourinho won during his time in charge at Stamford Bridge.
Marco Ianni, who is a second assistant to Maurizio Sarri, took great delight in seeing Ross Barkley snatch a 2-2 draw in stoppage-time.
He jumped off his seat upon seeing the ball hit the net and made a point of expressing his delight in front of Mourinho, who remained rooted to his bench.
Ianni swung a clenched fist in front of the Portuguese, who did not take kindly to being provoked at such an emotional moment.
Mourinho took off after his rival and had to be held back as players, staff and stewards all bunched together at the entrance to the Chelsea tunnel.