Teenage attacker Felix became the youngest player to score a treble in the competition's history on Thursday as he inspired the Primeira Liga leaders to a 4-2 victory over 10-man Eintracht Frankfurt in the first leg of their quarter-final tie.
The 19-year-old also tallied an assist for Ruben Dias' second-half header in a brilliant display that is sure to have alerted the heavyweight clubs that are believed to be tracking his development.
Manchester United are among the many sides reportedly interested, but Lage wants his emerging star to focus on getting better.
"Do not make him a superhero," Lage told Portuguese broadcaster Sport TV .
"Joao may no longer [seem] normal, but he is. He's a quiet kid. He goes out and has fun as if he was playing in a park.
"We have to give him peace of mind to grow. Then he will delight us.
"When he's even more consistent, he will be a fantastic player."
Benfica's cause was aided by Evan N'Dicka's dismissal in the 21st minute, the Frankfurt defender shown a straight red card for shoving Gedson Fernandes in the box.
Felix converted from the spot and impressed visiting coach Adi Hutter, who took confidence from the valuable away goals scored by Luka Jovic and Goncalo Paciencia.
"Joao Felix is a very intelligent player, who finishes play and creates. Benfica are very lucky to have him," Hutter said in his post-match media conference.
"He's a rare talent. In the second leg we will have to pay attention to him, but Benfica are not just one player.
"We have to play a perfect match at home, but I believe we can overcome Benfica. I was curious to know what it would have been like if we played with 11 men until the end.
"The two-goal difference leaves everything open for the second leg. Let's see what the result is, in a week's time, in Frankfurt."