Higuain is on the verge of a move to the Serie A club - worth an estimated total of 40million euros (£34.5million) - after he passed a medical on Wednesday, before Madrid's friendly with Lyon, which finished 2-2.
Carlo Ancelotti's side went behind to goals from Clement Grenier and Lisandro Lopez, before Morata pulled one back from the penalty spot, and midfielder Casemiro levelled with six minutes remaining.
Morata, who broke into the Real first team last year, paid tribute to the departing Higuain after the game.
He said: "Higuain always gave me a lot of advice and helped me, I wish him a lot of luck in his new adventure. I hope it goes well for him."
Higuain's sale means Madrid are left with three centre-forwards - Morata, Jese and Karim Benzema, and the young striker believes that the club do not have to replace Higuain.
"Karim, me and Jese and we can work well together," Morata said.
"But the club will have to decide if they want to sign someone else or not. It's up to them and they'll do what's in the club's best interests."
Twenty-year-old Jese agreed a new four-year contract with Real Madrid yesterday, and Morata believes it is a step in the right direction for both parties.
He said: "I'm delighted that he has renewed his contract, he needs to be at this club and to play for Real Madrid."
Despite only drawing with the Ligue 1 side, Morata believes the game was beneficial to the squad.
"This match helped us get back into the rhythm of playing. They scored two goals against us but we wanted to win and we showed good attitude on the pitch. We can be positive about the draw."
Casemiro, who signed a permanent move from Sao Paulo earlier in the summer after spending the latter half of last season on loan at Madrid, declared he will not be content to sit on the bench for most of next season.
"I want to continue fighting for a place in the team, my objective is to make the most of the opportunities I get in friendlies," he said.
"Ancelotti said he was happy with me and said to me: 'thanks for your efforts'. I've happy to have scored but the most important thing is the team."