Yamal made history in his country's opening game against Croatia by becoming the youngest player ever to appear in a European Championship game at the age of 16 years and 338 days.
He then claimed another piece of history by becoming the youngest player ever to score a goal at the Euros in Spain's 2-1 semi-final win against France, at the age of 16 years and 362 days.
Spain went on to beat England 2-1 in the final to win their fourth Euros on July 14, just a day after Yamal turned 17.
"He has done a really great job in the last year, he has improved a lot. What he did in the Euro is unbelievable," Flick told a news conference as he was officially unveiled as Barcelona's new coach.
"But great players maintain their performance and now it is necessary for him to keep his feet on the ground," he added.
"I think he is a great guy. I spoke with him before, when I arrived, and he is now in this team and of course, he gives us great moments but he can improve and make things better. He is on a really fantastic path."
Barca appointed the former Germany and Bayern Munich manager as head coach on a two-year contract in May after sacking Xavi Hernandez, tasking him with turning around the club's fortunes following their trophy-less run last season.
"What I want to see is that we are playing really good football, attacking football, and that everyone can see that this team really gives a lot for this club. I think this is crucial," Flick said.
"You can only win with the biggest clubs, which is why I am here. I am not saying that I will win every title like that but if we work hard we can achieve this," the 59-year-old added.
Flick, who led German giants Bayern to a historic sextuple of trophies in 2020, became the first coach ever to be sacked by the German national team in September 2023 after a string of bad results.
