The pair came together on track at Turn 6 in the early stages of the Qatar weekend’s third practice session on Saturday morning, as Espargaro tried to overtake.
Aprilia rider Espargaro gesticulated furiously at Morbidelli and later slapped him on his crash helmet when the latter motioned to him to calm down.
Espargaro was given a €10,000 fine and hit with a six-place grid penalty for Sunday’s grand prix, which will put him on the same row of the grid as Morbidelli.
However, Espargaro may not take part in the race after suffering a suspected fracture in his left leg after an incident in the sprint.
Morbidelli feels the FIM stewards’ punishment handed down to Espargaro isn’t strong enough and raged at the clash.
“This morning I was having my practice and then Alex Marquez crashed in Turn 2 and there was a yellow flag,” he began.
“So, [Jorge] Martin slowed down in front of me. I slowed down. But, by the time we reached Turn 4, Aleix overtook me. Then I overtook him back because I wanted to get back my original position.
“Then he overtook me like crazy into Turn 6, almost crashing and almost making me crash.
“When I was trying to tell him to take it easy because, after he banged on me, he got angry and started to make bad gestures, as he always does.
“When I was telling him to take it easy, to chill out, he did what you all saw. It’s a huge disrespect action towards me.
“It’s difficult to take, but I take it and the stewards have been analysing everything and took the countermeasures that they thought was right.
“According to me, they did nothing because what they did actually was to put him by my side for tomorrow’s race and make him race in today’s race as if nothing happened.
“So, for me they did nothing - what he did today was such a big disrespect towards another competitor, in other sports it would have been treated in a much different way. So, it’s OK, I keep going.”
When it was put to him that Espargaro’s reaction seemed strange for a practice session that counted towards nothing, Morbidelli was scathing against the Spaniard.
“You’ve seen him overreacting many, many times in his career,” he added.
“He has much more episodes to be ashamed of than to be proud of. I wonder what he will say to his kids.”
However, Morbidelli didn’t want to be drawn into what penalty he thought would have been suitable.
“I don’t want to say what’s an appropriate punishment, but putting him by my side in tomorrow’s race is joking with us,” he said.
“Also, this is disrespectful, because they gave him exactly six positions for tomorrow’s race and he will be by my side.
“I want to see him 100 metres from me always - instead, he will be by my side.”
Espargaro has cancelled all of his media duties for Saturday after the fracture in his leg was discovered.
However, Espargaro took to Instagram to comment on the incident. He concedes he had "a very bad reaction" to Morbidelli in the moment, but feels his penalty was "too much".
"It has been a day to forget, first of all the incident with Morbidelli," he began.
"I had a very bad reaction. He was walking in the middle of the track, he almost hit me twice, he was on the line, he didn't let me enter again and I lost my temper with a totally disproportionate reaction.
"And for that I received a penalty. From my point of view [it is] too much, but I accept it because, obviously, the image is not good."