The 19-year-old Mercedes driver's triumph at Spa last weekend increased his championship advantage over Ferrari's Lewis Hamilton to 45 points but there were elements of the Italian's driving that father Marco, despite his obvious delight at the outcome, felt could be improved.
The number of times his son needlessly exceeded track limits, risking a sanction, was a concern.
"One of the first things he told me after the race was congrats but, always a but, 'if I see you doing another track limit for nothing I'm going to stretch your neck like a chicken'," Antonelli laughingly told reporters at the Hungarian Grand Prix.
"Those were his words. So it's something I need to definitely work on."
Antonelli recognised he liked "to use the track sometimes a bit too much".
"I mean, I look back at Spa and the two track limits (violations) I did were very stupid and I was like 'what the heck am I doing?'" he said.
"It's a bit like Barcelona as well and Miami. I just feel that it's something I need to work on for sure because sometimes in a race I might need to use them but if I use them when I don't need to then I might find myself in trouble."
Antonelli has won six of 10 grands prix this season and is 50 points clear of teammate George Russell, who has won twice but suffered three races without scoring - spinning off into the gravel on the opening lap at Spa.
Russell suffered a loss of straight-line speed in Belgium but told reporters at the Hungaroring that Mercedes had now got to the bottom of the problem.
The Briton was complimentary about Antonelli's form.
"At the moment Kimi definitely deserves to be leading the championship," he said. "He's done a better job than me this season. That's the facts of it.
"The last two weekends were challenging for me when maybe my performance is not where it needs to be.
"But then when there's something external hampering that as well, it's difficult to know where you put your attention to. So I'm hoping just for a cleaner weekend here."