Murray spoke to Kyrgios after the match in which the Australian abused and swore at Fergus Murphy and called him the worst umpire in the game.
He was fined $113,000 (£93,254) for five separate offences.
“It wasn’t good, and I felt for Fergus as he shouldn’t have to put up with that,” Murray told BBC Sport.
Kyrgios, 24, smashed two racquets in a corridor by the side of the court and called Murphy a “tool” in Wednesday’s second-round match.
“I chatted to him a little bit last night after the match,” said Murray, who has developed a strong bond with Kyrgios.
“It’s obviously up to him, and I think for the most part a couple of weeks ago in Washington [where he won his sixth ATP title], he did a good job of helping himself and using the crowd.
“But obviously this week, he went back to what he was doing before. You just hope he will figure it out, because a week like in Washington is really good for Tennis, but last night isn’t. Hopefully he gets it figured out.”
Kyrgios is now waiting to discover whether the ATP thinks he has committed a “major offence” under the player code. If so, he could face a further fine or even suspension from the tour.
The Australian took part in a light-hearted practice session late on Thursday afternoon before heading to court three to watch Murray and Feliciano Lopez beat Ryan Harrison and Jack Sock in the doubles.
That match was also officiated by Fergus Murphy.