On Saturday afternoon in the weekend's third practice session, Espargaro slapped Morbidelli on his crash helmet after the pair came together at Turn 6 while the former was attempting an overtake.
Espargaro was handed a six-place grid penalty for the grand prix and a €10,000 fine, while Morbidelli launched a scathing attack on the Aprilia rider on Saturday evening.
Speaking to the media on Sunday, Espargaro said he was "ashamed" of his behaviour, but feels Morbidelli is a repeat offender in getting in riders' ways on track, highlighting several incidents in Malaysia the week before.
"I said before, [the] first thing is I'm very sorry and ashamed of my outburst for my team and myself," Espargaro began.
"Obviously, if you just saw the last part of the story I fully accept the responsibility. It was not my idea to punch him or whatever, it was just my idea to make him go away.
"It was my mistake, but in my opinion, it's not fair just to watch the last five seconds. For me, Franco, it's one year and a half that he is cruising all around the world on tracks.
"It's his attitude, he has no respect for anybody. Last race it was with his team-mate, [there was] no penalty.
"Also with Marc, calling him like a dog. Yesterday to me three times. After he impeded me three times, I was trying to go back on track and he was not allowing me to go in the track.
"Then I reacted very badly. I'm sorry for my reaction, but I think it's not really fair to judge the last five seconds.
"And then the thing that I'm more angry about, and this will not finish here, is to the press he talked about my family and my sones.
"And for me, this is not fair, what he did. He went over [the limit]. I'm very angry."
Espargaro suffered a small fracture to his leg in a crash in the sprint, which ultimately forced him to pull out of the grand prix in Qatar seven laps in.
While the pain was a problem for him in the warm-up, Espargaro says the real issue was the build-up of blood in the injury area.
"I mean, I have a fracture, quite important fracture in the peroneal," he said.
"The problem is not really the fracture. The problem is that everything is full of blood, the ligaments, the muscles, everything.
"So, it's like a compartment feeling. I got a bump of drugs to try to avoid the pain because this morning [in warm-up] it was impossible to ride due to the pain.
"In the race I didn't have pain, but I had no power on the foot because everything was full of blood.
"So, my leg was completely locked and I decided to stop in the garage. It was impossible for me to go up and down in gearing."
