The verbal sparring continued at the next change of ends as Kyrgios queried whether he meant "borderline good or bad" and was told "you know exactly what I meant, Nick".
Woodbridge's comments come after Kyrgios's prolonged exchange with the chair umpire at the Shanghai Masters during his first round defeat to American qualifier Bradley Klahn.
But he also sounded a note of caution.
Stan Wawrinka and Nick Kyrgios were among the players to make a first-round exit at the Shanghai Masters on Monday.
Only through understanding work ethic and scheduling, creating the right team around himself, only then can you unlock the potential really..
Doubles great Woodbridge says Kyrgios, who this week lost the top Australian ranking to Alex de Minaur, gets singled out.
Kyrgios was fined after he stormed off mid-way through his first-round exit in the event past year, while in 2016 he argued with spectators and was accused of giving away points in another defeat.
"But there is still a process in place that he needs to do like any other player needs to go through in order to be successful", he added.
He left the court using his mobile phone.
Dumusois called Kyrgios out for lackluster play at one point, saying his efforts were "really borderline" during the second set.
The match didn't go unnoticed as chair umpire Damien Dumusois appeared to be accusing Kyrgios of tanking at the beginning of the second set - which didn't sit well with the Australian.
Later, after belting down an ace, Kyrgios sarcastically asked Dumusois: "Was that borderline?" "I don't want to talk about that any more".
Ranked 104 in the world, Klahn presented few problems for Kyrgios in the first set and he looked on course to take out the match.
In 2016, he was banned for eight tournament weeks and fined a total of $41,500 after he was beaten 6-3, 6-1 by Mischa Zverev in a second-round match in which Kyrgios put in a series of half-hearted serves and appeared to be walking off court before the unseeded German had returned the ball to him.
The 23-year-old quickly responded to Dumusois by saying: "I don't care, bro".