The Australian star beat home favorite Paul Jubb 3-6 6-1 7-5 6-7 (3-7) 7-5 in an entertaining match, but felt one supporter overstepped the mark in his heckling.
After winning match point, Kyrgios turned towards one of the stands and spat on the floor as he made his way to the net.
When asked by a reporter if he did spit in the direction of that fan, Kyrgios replied: “Of one of the people disrespecting me, yes. I would not be doing that to someone who was supporting me.
“I’m okay with receiving a lot of it [heckling]. What I do not understand is as soon as I give it back, for instance in Stuttgart I gave it back, and I got a game penalty.
“As soon as I won the match, I turned to him. I’ve been dealing with hate and negativity for a long time, so I do not feel like I owed that person anything.
“He literally came to the match to just not even support anyone really. It was more just to stir up and disrespect.”
Kyrgios had said earlier this month that he was racially abused by a member of the crowd at a tournament in Stuttgart, which the organizers said they were investigating.
The Australian said he was not racially abused on Tuesday, but was concerned about the frequency of fan abuse.
“I’m just starting to think it’s normal when it’s really not,” he told reporters. “I did not say anything to the crowd until they started just every time I came down to the far end. I do not know if it is normal or not.
“It’s got nothing to do with Wimbledon. I just think it’s a whole generation of people, like on social media, feeling like they have a right to comment on every single thing with negativity. It just carries on to real life.
“Because there’s a fence there and I physically can’t do anything or say anything because I will get in trouble, so they just feel that they can just say anything they want.”
That was not the only flashpoint of the match, as Kyrgios was also unhappy with a line judge’s call on a point in the opening set.
He later said during his press conference that umpires at Wimbledon should be younger as “factually people who are younger have better eyesight.”
Krygios is scheduled to play doubles with Thanasi Kokkinakis on Wednesday, before continuing his singles campaign against 26th seed Filip Krajinović on Thursday.