They were not the only drivers to fall out during the race, with Daniel Ricciardo unhappy with his Red Bull team mate Max Verstappen.
Renault's Hulkenberg and Haas Ferrari's Magnussen were in a battle for 11th, when Hulkenberg attempted to sneak past Magnussen on the outside of the corner.
"Hulkenberg was overtaking Magnussen around the outside of Turn 2 on Lap 62", said the Stewards.
In finding Magnussen guilty of an illegal block, the Hungaroring race stewards added two penalty points to Magnussen's licence, taking to him within five of a race ban, and demoted the Dane from 11th to 13th.
The confrontation was triggered by a controversial on-track clash in which Hulkenberg was forced wide as he tried to overtake Magnussen at Turn Two of the Hungaroring.
Steiner however says his driver was right to be rude.
Manager admits he would break world record transfer fee for Tottenham star
Chelsea boss Antonio Conte is a "big fan" of Tottenham Hotspur defender Danny Rose , according to The Mail . The club recently signed Alvaro Morata from Real Madrid in a record £60m deal.
Hulkenberg apparently still had a chip on his shoulder after confronting Magnussen, as the Renault pilot continued to insult him in later interviews, according to NBC Sports' Will Buxton.
"Suck my balls honey", came the reply.
"I congratulated him for being the most unsporting driver of the whole grid once again", Hulkenberg said.
"When it comes to racing, he's just nasty". Hard defending is fine but, when he does this, it's just ruthless.
"Sending people into the wall and what he did there, opening up the steering and making me run wide, it's just being an arsehole basically".
"We had really nice words, he said [suck my balls], that was his return, so it's quite interesting with him, yeah".
The German revealed that he intends raising the matter with (Race Director) Charlie Whiting.
- HSBC to launch $2 billion buyback as profit up 57%
- Mo Brooks Don't Want Mitch No Mo
- Neymar storms out of training after bust-up with teammate
- Jamie Carragher claims Coutinho has wanted to leave 'for months'
- Five dead after vehicle bomb explodes near police station in Mogadishu
- Trump To Republican Senators: 'Don't Give Up'
- Barca wins first Clasico of the season
- IndyCar 2017: Josef Newgarden wins Honda Indy 200 at Mid
- Shocking footage shows French airport worker hitting passenger holding baby
- Kim and Webb defy wild Scottish weather