The Swiss three-time major victor and former world number three, a wildcard in this tournament, was beaten 4-6 6-4 6-3 by 13th seed Borna Coric.
The verbal sparring continued at the next change of ends as Kyrgios queried whether he meant "borderline good or bad", and was told that his efforts left a lot to be desired.
"I think it's really up to him where he wants to go and what his potential really holds", the 20-time Grand Slam victor said.
"We don't really know and I don't think he really knows exactly what his potential is".
Fritz, a qualifier in Shanghai who is ranked 60th in the world, also had 14 aces.
The Australian, who at times appeared largely disinterested in his three-set loss to American qualifier Bradley Klahn, fired back telling chair umpire Damien Dumusois he "didn't care" for his opinion and "you have no right to tell me that it's poor".
The 23-year-old Kyrgios made another contentious exit from the Shanghai Masters on Monday after a running argument with the chair umpire who suggested his efforts were "borderline".
Kyrgios then smashed an ace and turned to Dumusois to sarcastically ask "was that borderline poor?" and was rebuked.
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But she appeared to reinforce the party's red line on checks along the Irish Sea in the event of the backstop taking effect.
But a sloppy service game down 4-5 cost Kyrgios the set and he unravelled from there amidst a stretch of five lost games.
Past year he was fined $US10,000 for unsportsmanlike conduct after hitting two balls out the stadium and quitting mid-match against Steve Johnson in the first round of the tournament. Federer warns Kyrgios Roger Federer warned temperamental Australian Nick Kyrgios on Tuesday that he would never fulfil his potential without the work ethic to go with his talent.
"I'm not going to do it, but I'm just saying".
Shanghai is not the only scene of a Kyrgios controversy.
And in 2015, he was fined USD1,500 for using obscenities during a match and calling the event a "circus".
Last week, Kyrgios ceded his spot as Australia's highest-ranked male player to Alex de Minaur following a defeat at the Japan Open.
The Swede climbing down from his chair in NY to have a lengthy chat with Kyrgios when he was showing little effort as he trailed by a set and 3-0 down against Pierre-Hugues Herbert.