Andreas Seidl admits there is a "fundamental risk" that McLaren could lose its most competitive driver for a race.
In Austria, a penalty for the on-form Lando Norris moved the British driver dangerously close to the maximum 12 super licence penalty points.
Once his tally reaches 12, a race ban is mandatory.
"It is not reassuring. There is a fundamental risk," team boss Seidl told RTL.
However, as beating Ferrari to third place in the constructors' championship is the team's primary goal for 2021, Seidl said Norris should keep on pushing for "maximum performance" without being "too crazy".
Looking forward, Seidl said the FIA should re-consider the current license points system.
"It cannot be in the spirit of Formula 1 that a driver has to sit out a race for the kind of incident we saw in Spielberg," he insisted.
Seidl agrees that license points penalties are "right and important" but only when it comes to "drivers doing dangerous things".
He predicts that the matter will be discussed behind the scenes at Silverstone next weekend.
"Hopefully we will then find another solution for the future," said the German.
As for who would replace Norris in the event of a ban, Seidl revealed: "We have an agreement with Mercedes regarding the reserve drivers."
He said the "first choice" would be former McLaren driver Stoffel Vandoorne.
