The 19-year-old forward joined Diego Simeone's Atletico from Benfica in a €126million move last month and has turned in some dazzling pre-season displays.
As such, his famed Portuguese compatriot Mourinho believes there will be a demand for instant results.
"He has a challenge due to the extent of his talent and because of the investment the club have made on him," Mourinho told the Portuguese Football Federation's (FPF) television channel, Canal 11.
"I believe that he can't escape this responsibility. It doesn't matter if he's 18, 20 or 25.
"What matters is his talent and the responsibility he has."
That responsibility extends to spearheading a challenge for the top honours in Spain and Europe, according to Mourinho.
Despite losing Lucas Hernandez, Rodri, Diego Godin and Antoine Griezmann - the France star's long-anticipated move to Barcelona eventually coming to fruition – Atletico have reinforced impressively.
Kieran Trippier, Marcos Llorente and Hector Herrera are among those to have bolstered Simeone's squad and Mourinho feels they must now look to match Spain's heavyweight duo.
"Atletico Madrid's level of investment leaves them with responsibility to fight for the Champions League and LaLiga," he said.
"It's clear that Barcelona and Real Madrid have to be there because of their power, financial capability, culture and quality.
"Atletico in recent years have been without this responsibility, but the level of investment they've made is incredible.
"It's time to say, 'We're here, we're big, we want to be big and we are here to win'."
Atletico begin their LaLiga campaign at home to Getafe on Sunday.