Gunther Steiner says both the Mick Schumacher camp and the media should keep their celebrations muted after the struggling German driver ended his points drought at the British GP.
Prior to the breakthrough, after which Schumacher celebrated with his family and team, rumours had been swirling about whether the 23-year-old would be offered a new Haas contract for 2023.
But even before the maiden points, team boss Steiner had warned that "one swallow does not make a summer".
"You can't say you want to finish eighth either," Steiner told Sport1.
"That's not a goal. That's why the podium is the next goal.
"These drivers are all human beings and there are 19 others who are great. And nine other teams that have good cars," he said.
He said striking the balance between depression and euphoria is always his goal, which explains his comments about not going over the top about 4 points.
"That's exactly what I meant, in a positive way," said Steiner. "One swallow doesn't make a summer to keep the pressure off.
"It's just about keeping your feet on the ground, staying calm, not putting too much pressure on Mick from the outside - that it always has to work out now, because then we wouldn't have achieved anything again.
"But I think it's easier for him now. He didn't have that much pressure already in Canada, so we have to keep going like this.
"But putting him up on a pedestal and then throwing him off again - we shouldn't do that," Steiner insisted.
As for whether Schumacher's first points make a contract extension more likely, the Haas chief would not be drawn.
"As a team, we always either confirmed or didn't confirm our drivers until after the summer break," the 57-year-old told the German broadcaster ntv.
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