Murray told Fognini to 'Shut up' during the third set of the 7-6(4), 2-6, 7-6(2) encounter, won by Fognini, and pushed the Italian's hand back during the handshake.
Speaking to press, Murray explained that the incident began when Fognini apparently attempted to distract the former No. 1 during a volley.
"Someone made a noise, I didn't know who made the noise, I looked in the direction of where the noise came from. He then told me, 'Stop looking at me, what are you looking at me for.'" said Murray. "I was like, 'I was just about to hit a shot and someone made a noise.' He then told me to stop looking at him.
"He told me to stop complaining, to have a sense of humor. I wanted to know where the sound came from and it came from him, which you're not allowed to do."
Murray was also unhappy with Murphy's reluctance to get involved.
"He wasn't saying anything to him. I was obviously frustrated with that," said Murray, adding of Fognini. "He wanted to engage with me, I probably shouldn't have done but I'm not having him talk to me like that on the court"
The three-time former champion also criticized his own performance, having serving for the match twice. But he came away satisfied with his three events in China, having secured his first Top 20 win and first Masters 1000 singles victory since right hip resurfacing surgery.
Murray is still a long way down in the rankings, and another British player, Kyle Edmund, has also dropped to No. 42 from a high of No. 14 in 2018.
Edmund has lost his past six singles matches. (Getty Images)
In Shanghai, Edmund fell in the first round against Jeremy Chardy, and has had knee problems this season.
“He's obviously been going through a tough time just now,” Murray said following his first-round win. “I think he's been feeling a bit better physically recently, but obviously this year has been a little bit stop-start for him and it's tough. I mean, tennis is a hard sport. When you start losing matches, you're playing at this level, it's difficult. The only way to sort of turn it around is to keep getting yourself competing and training hard and practicing the right things.
"It will turn around for him, because he's a really, really good player, and he has a big game. So I'm sure he'll turn it around, but that only comes with working hard.”
The 32-year-old Murray is scheduled to next compete at the ATP 250 event in Antwerp.