Costa has scored six goals in 14 appearances for Atletico after the club's transfer ban expired in January, allowing him to complete his move from Chelsea, while Morata - effectively Costa's replacement at Stamford Bridge - netted his first goal since Boxing Day in Sunday's FA Cup win at Leicester City.
Despite that dip in form, Costa has backed Morata to come good.
He told a news conference: "I miss Morata, we have a great relationship. He is a great person and a great player. He is having a bad time but is starting to score goals again.
"Hopefully we can play together because competition with him is not a problem. The pressure [for him] is the same, being a striker in the national team means a lot."
Costa's last international appearance came in June 2017, shortly before he was frozen out at Chelsea by manager Antonio Conte, and the 29-year-old admits Lopetegui was honest about where he stood during his period away from first-team football.
"He was very clear with me, as with all the players: if you do not play, it is impossible to call you up.
"He also told me that when I returned the doors would be open and here I am. I thank him for his trust."
Costa is hoping to impress over the next week to ensure he is on the plane to Russia for the World Cup, which gets under way in June.
"These are two very important matches, I am still not in Russia," he said.
"I hope things go well and I continue to grow with my team so that I can be here again."