The two youngsters had impressive tournaments at the Copa America and Euro 2024 respectively.
Garnacho was a bit part player for Argentina, who won the tournament by beating Colombia in the final on Sunday.
Ten Hag, referring to the club's academy players, said: "At least, I want to see they're acting like Manchester United (players), so hard to beat, team spirit, showing energy, intensity.
"That is the least I expect, but I told them in my team talk, which I gave yesterday, look at the Copa America final involving Alejandro Garnacho.
"Unfortunately, he didn't play and that's his next challenge, to become a starting XI player, like Lisandro Martinez has, and the Euro final yesterday with Kobbie Mainoo.
"Last season in the same game (first pre-season match), Kobbie Mainoo was part of it, so for them it's also possible, but they have to earn the right to play in the first-team of Manchester United.
“You don't get it - you have to earn it. We have a mixed group and the senior players must get match fitness and guide the youngsters, help and support them."