Trailing 40-30 in the second game of the second set, Simon exchanged words with umpire John Blom after walking to his chair.
"I don't want to play, when it's raining, on grass. That's it," he was heard saying, before adding: "If I play and get injured, I will sue you and you will pay."
A large number of matches scheduled for days two and three of The Championships were delayed by rain, though better conditions allowed for a prompt start to play on Thursday morning.
But Simon -- who went on to lose 6-3, 7-6(1), 4-6, 6-4 to Dimitrov -- was unhappy with having to play on when drizzle passed over the All England Club just after 1.30pm.
He later told a press conference: "I hate to play when it's raining. I never understood when they are forcing us to go on the court when the court is slippery. I understand. It's just not acceptable for me.
"I feel the day I'm going to get injured on slippery grass, I'm going to sue everyone in the stadium. We try to understand what is happening in both parties, like tournaments and players, but in one point yesterday it was just ridiculous.
"The supervisor told me, 'It's raining but the water is not going to the ground. It's really light rain and it's there and it stays in the air and it's flying away. So the grass is not wet'. And I have to answer that. So in the match you just see me on TV, I'm pissed because I want to destroy him."
Simon said he will discuss the issue with ATP Player Council, of which he is a member, and also criticised the players' treatment during the Australian Open.
"It's happening in basically every slam, so it's not just here," he added. "Here it's always about the grass that is wet. But in Australia they force us to play when it's 44 degrees and the doctor says, 'Yeah, it's fine'.
"The tournament just got lucky nothing really serious happen once on the court for a player, like someone breaking his leg on slippery court or someone feeling really bad in Australia when it's 44.
"They just try to push. They want us to play. We are just human, or maybe they are just really confident that we are that strong that we can play anywhere. But on my side, I play, it's slippery. We all have a bad feeling, we want to stop.
"It's always on the tournament side. They always force you to play and you cannot say anything. You discuss. You say, 'Come on, the grass is wet'. And then you have the famous water that is not touching the grass reason that force you to play. It's complicated.
"We are going to have more and more discussion about it [on the ATP Player Council]. We really understand when it's a terrible day for the tournament and there is no showing for the public, they stay long and they want to see the match. But it's just not possible.
"I think unfortunately we should stop. It looks pretty simple, like you see the rain on grass, you say, 'OK, we stop'. That's basic. But it doesn't sound basic on the other side."
Dimitrov was more diplomatic afterwards. He said Simon is a "cool guy" and that they have mutual respect.
"Everyone has their own way. I understand his frustration," the Bulgarian told a press conference. "But it's the same for me. We have all the officials out there. We had the umpire coming down, the supervisor, so all these guys are taking unbelievable care of us, to protect us and to take the right decisions
"I know when there is a little mist in the air, the grass is a little slippery. That's logistics, yes. And you just try not to push too much, so you don't want to slide. You have to be a bit more cautious. You can't fight the weather."
Several first-round games, which had been delayed due to the rain, were also finished Thursday. Among them, Donald Young beat Florian Mayer, Lucas Pouille saw off Marius Copil and Australian qualifier Matthew Barton won a deciding set with Albano Olivetti 14-12.
John Isner also won his first-round match 7-6 (2), 7-6 (5), 6-3 against Marcos Baghdatis, while sixth seed Milos Raonic, who reached the final at Queen's, progressed to the last 32 with a 7-6(5), 6-4, 6-2 victory over Andreas Seppi.
Croatian Ivo Karlovic, the 23rd seed, hit 34 aces but was beaten 6-3, 3-6, 7-6(5), 6-4 by Slovakian qualifier Lukas Lacko, the Slovakian qualifier. Elsewhere, Denis Istomin secured a 6-4, 7-6(5), 6-2 win over Nicolas Almagro.
PA Sport contributed to this report